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 Assignfrom 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.
You want your middle-grade students to complete the pre-algebra math topics so they are ready to begin to study algebra in 8th or 9th grade. A disheartening number of middle-grade students have not memorized basic multiplication facts (times tables). Students must know multiplication facts to follow, absorb, and implement pre-algebra topics. How to teach multiplication facts to struggling students? How can a teacher help their struggling students learn multiplication facts when a lot of their students do not need to do that work?
Rocket Math Online Game includes learning tracks for pre-algebra skills as well as basic multiplication and division facts. Within the Rocket Math Online Game, teachers assign students the learning tracks that they most need.
Math Strategies for Struggling Students
Students who do not know their multiplication facts are constantly distracted from learning math strategies by having to stop and “figure out” basic facts. Every time they are asked to provide the answer to a multiplication fact, they have to turn their attention to working it out or looking it up. By the time they have gone through their process, they have lost the thread of the strategy they are supposed to be learning. The most important thing a math teacher can do for struggling math students is to help them bring math facts to automaticity. Then answering math fact questions no longer interferes with learning multi-step strategies for solving math problems.
Why Multiplication facts are Important to Learn Before Middle School Math
Many pre-algebra math topics assume students have a ready knowledge of multiplication facts to even understand. When I was a middle-grade teacher, my remedial students were unable to follow or understand topics such as Finding factor pairs, reducing fractions, equivalent fractions, converting fractions, unlike fractions, and so on. I realized that it was because they did not know basic multiplication facts. When I reduced 8/24 to ⅓ it was like magic because they did not quickly recognize the multiplication facts involved. They didn’t understand the concepts we were trying to learn because they did not see the relationships they were supposed to know. When I asked them to think of the factor pairs of 36 they were unable to find them all, no matter how much time I gave them. While students can do multi-digit multiplication problems using a times table chart, it does them no good in pre-algebra topics because it takes too long, even if they know what to look up. Now let’s look at how to teach multiplication to struggling students using Rocket Math Worksheets or Rocket Math Online Game.
How to Teach Multiplication to Struggling Students Using Rocket Math
Students who have not yet mastered multiplication facts are going to require a very effective teaching methodology to learn them. The haphazard, leave-it-up-to-the-student methods have already failed them. By now, these students lack confidence in their ability to learn the facts, so you need a sure-fire system.
Rocket Math is just such a system. Both the Worksheet Program and the Online Game systematically introduce students to the facts in a careful sequence that they can do. The Worksheet Program and Online Game ask students to memorize only two facts and their reverses at a time.
Students demonstrate mastery of those facts by answering them without hesitation. Then Rocket Math will add two more facts and their reverses. Small steps at a time, systematically the students can memorize the facts and answer them instantly from memory. If students practice every day, within a few weeks you’ll see a dramatic improvement in their recall of multiplication facts.
But what about the students who already know their multiplication facts? Rocket Math has something for them as well.
Rocket Math Programs for Advanced Students
Teachers can assign Rocket Math as a 10-minute warm-up or cool down for all their students whether they are behind or advanced. Rocket Math has several pre-algebra topics for those students who already know their multiplication facts. Each of these topics will help them do pre-algebra processes more fluently and to quickly recognize relationships that they have memorized.
When students initially learn about fractions they are often only shown proper fractions. As a result, they have a limited understanding of fractions and can be confused by improper fractions or mixed numbers. The Rocket Math programs (both Worksheet and Online) prevent this problem. From the start, we teach students using examples of both proper and improper fractions as well as whole numbers and mixed numbers. Students learn to identify over 90 different fractions quickly and easily by getting lots of practice. Their understanding of fractions will deepen and become more flexible as they learn to recognize many examples of fractions.
Students will memorize the most common equivalent fractions with this Rocket Math Learning Track. They will also learn to identify a number of fractions, such as 2/9, that do not “reduce” or for which there are no equivalent fractions in lower terms. Students also learn to recognize a fraction equal to 1 whole in its various forms. When students don’t instantly know the answer they are told the equivalent fraction and given practice on it. The computer gives help in the Online Game. Their partner gives that help in the Worksheet Program. By the end of the program, students will learn over 90 equivalent fractions. This gives students an excellent start on being able to manipulate fractions quickly and easily.
Students are required to “find the factors” when dealing with unlike fractions and reducing fractions. Rocket Math Worksheet and Online Game teach students how to find factor pairs. Students learn how to find all the factor pairs and what they all are for many common numbers. They also learn to identify prime numbers and their characteristic of having only one and themselves as factors. Students learn the factor pairs in order and know the “last” factor pair when they see it. When the game asks “What’s next?” students can provide the next pair of factors or click the checkmark to indicate there are no more factors. When students go through this Learning Track they will no longer hesitate when asked for the factors of common numbers.
Learning Track 16: Fraction & Decimal Equivalents
Common fraction and decimal equivalents should not require a laborious process to “figure out.” Students should just know these, so this Learning Track in the Online Game allows them to memorize a bunch of common decimal and fraction equivalents. Having a facility with a lot of fraction and decimal equivalents means faster computation as well as a way to check their process when manipulating fractions and decimals. Students also learn another essential pre-algebra skill that often confuses them. They learn to correctly and fluently translate a fraction into a division problem and vice-versa.
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
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.
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.
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!)
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.
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 asRocket 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?
TheRocket 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.
Addition 1s through 9s
Subtraction 1s through 9s
Multiplication 1s through 9s
Division 1s through 9s
Fact Families (+, -) to 10, ex.4+6, 6+4, 10-4, 10-6
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.
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.
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.
You’re probably looking for a math facts test online to evaluate how well your students are learning their math facts. But did you know, it’s more effective to teach and test at the same time? Rocket Math’s online game does exactly that, making it the ultimate math fact online testing app.
Testing without teaching doesn’t work
Too many math facts tests online spend a lot of time asking students facts they don’t know. As a result, students learn inefficient ways to solve math fact problems, like counting on their fingers. Even puzzling out answers from knowing doubles is tedious. Students will find memorization of math facts difficult if they constantly have to “figure out” math facts. Plus these two methods are slow, setting students up to fail timed math fact tests in class.
So what is the best way to test whether a student can recall math facts?
Teach and test a small number of math facts in tandem
An effective math facts test online will start teaching as soon as the test finds the first math fact that the student can’t answer quickly.
It is important to begin teaching immediately for several reasons.
(1) Students think that they will always have to compute math facts on their fingers or with a number line. They don’t know that they can and should get to a point where they instantly recall the answers to facts. Helping students memorize a previously unlearned math fact immediately after they miss the problem shows them that they can successfully master any fact.
(2) Students need to know that we do NOT want them endlessly figuring out math facts. By responding immediately with teaching, we send the message, “Hey, you didn’t know this fact instantly. That’s not what we want. Let’s practice this one, right now, so you can learn it.” Requiring the student to answer the fact again faster reinforces the message.
(3) Teaching a fact works best when the fact is surrounded by facts the student already knows. Therefore, the best time to teach is when a student meets the first math fact they can’t instantly recall. An effective test online will mix the unrecallable math fact with a sea of already mastered material, teach the math fact, and then test it again.
(4) The student learns the difference between memorized and unmemorized facts. This helps the student understand that the goal is to instantly recall that fact.
(5) With a combined teaching and testing approach, a student’s success rate will be high since the student primarily answers facts they already know. As a result, students are motivated to learn more math facts.
Why testing and teaching is the perfect learning paradigm
If your teaching program works carefully in sequence, students will encounter opportunities to practice facts they know (a good thing!). Gradually, new facts will be introduced, practiced and tested. That is the perfect recipe for successful learning. Over time, students will be able to master all the facts as the program works through its sequence. Now you have accomplished the end goal: for students to learn the facts they didn’t know. By testing and teaching as you go, students remain encouraged, learn the difference between problem-solving and memorization, and reach mastery.
Rocket Math game: the ultimate math fact test online
The picture to the right shows me watching the very first kid try out the Rocket Math online game. As soon as he saw math problems, he said, “I don’t really like math that much.” But he saw the problem on the screen was 3 + 1 =, so he just typed in 4 because he knew the answer. Then he saw 2 + 1 = and he says, “Well I know that,” and he typed in that answer. The reverses (1 + 3 and 1 + 2) came up and he could answer those. The online math app only introduced those two math facts and their reverses, but he had to answer twelve in a row to pass the test.
Over time, he became faster. He answered all twelve math facts and received an on-screen congratulations. Mission Control (a fictional character in the math app) told him that he had “taken off with Set A” and could, “try for orbit” if he dared! After finishing the round, he brought the tablet over to me and said he liked it and wanted to play it again as soon as the mandatory 30-minute break was over.
Not only did the Rocket Math app teach and test four math facts in 5 minutes, but the student wanted to continue practicing math facts. That’s the beauty of a combined teaching and testing approach. Kind of a big deal, eh?
There are plenty ofmath facts apps out there that let students practice math facts they have already learned. Few apps actually teach math facts. But apps from Rocket Math and XtraMath are exceptions. While both apps teach students math facts, one is more effective and fun.
The two best apps for actually teaching math facts
Math facts apps from Rocket Math and XtraMath effectively teach math facts because they have four essential characteristics:
Both math facts apps require students to demonstrate fluency with facts. Fluency means a student can quickly answer math fact questions from recall. This is the opposite of letting a student “figure it out” slowly. Neither app considers a fact mastered until a student can answer a fact consistently within 3 seconds.
Both math facts apps zero in on teaching (and bringing to mastery) a small number of facts at a time. This is the only way to teach math fact fluency. It’s impossible for students to learn and memorize a large number of facts all at once.
Both math facts apps are responsive. Apps simply do not teach if they randomly present facts or do not respond differently when students take a long time to answer a fact.
Both math facts apps only allow students to work for a few minutes (less than ten) before taking a break. Teachers and parents may want to keep students busy practicing math facts for an hour, but students will come to hate the app if they have long sessions. A few minutes of practice in each session is the best way to learn and to avoid student burnout.
Both math facts apps re-teach the fact if a student makes an error. While both Rocket Math and XtraMath re-teach facts, they re-teach them differently.
While both apps contain these important features and teach math facts, there are a few vital elements that make an effective app like Rocket Math standout.
An effective app gives a student a sense of accomplishment
The difficult thing about learning math facts is that there are so many to learn. It takes a while and students have to persevere through boring memorization tasks. The best way to help students learn their math facts is to give them a clear sense of accomplishment as they move through each task.
How XtraMath monitors progress
To develop a sense of accomplishment among its app users, XtraMath displays math facts on a grid. XtraMath tests the student and marks the ones that are answered quickly (within 3 seconds) with smiley faces. It takes a couple of sessions to determine what has been mastered and what hasn’t, so there isn’t a sense of accomplishment at first. This grid is displayed and explained, but it’s not easy to monitor progress. Over time, there are fewer squares with facts to learn, but there isn’t clear feedback on what’s being accomplished as students work.
How Rocket Math monitors progress
Conversely, Rocket Math begins recognizing student progress immediately and continues to celebrate progress at every step. The Rocket Math app begins with Set A and progresses up to Set Z. Each lettered set has three phases: Take-Off, Orbit, and the Universe. That means there are 78 milestones celebrated in the process of moving from Set A to Set Z.
Take-Off phase has only 2 problems (and their reverses) repeated three times. The student just has to get all 12 correct to move on. When the student does that, the doors close (with appropriate sound effects) to show “Mission Accomplished.” They also are congratulated by Mission Control. “Mission Control here. You did it! Mission Accomplished! You took off with Set A! Go for Orbit if you dare!” With this type of consistent (and fun!) recognition, students clearly understand that they are progressing, and they get the chance to keep learning “if they dare!”
In addition to the three phases, students progress through the sets from A to Z. Each time a student masters a set, by going through all three phases, the student gets congratulated and taken to their rocket picture, as shown above. When a level is completed, the tile for that level explodes (with appropriate sound effects) and drops off the picture, gradually revealing more of the picture as tiles are demolished.
In the picture above, the tile for “N” has just exploded. After the explosion, a student is congratulated for passing Level N and encouraged to go for Level O if they dare. When you talk to students about Rocket Math, they always tell you what level they have achieved. “I’m on Level K!” a student will announce with pride. That sense of accomplishment is important for them to keep chugging along.
An effective math facts app correct errors—correctly
Neither of these math fact apps allow errors to go uncorrected. Students will never learn math facts from an app that does not correct errors. That puts these two apps head and shoulders above the competition. However, these two apps correct errors very differently.
How XtraMath corrects errors
On the left, you can see the XtraMath correction is visual. If a student enters the wrong answer, the app crosses the incorrect answer out in red and displays the correct answer in gray. A student then has to enter the correct answer that they see. This is a major mistake. In this case, students don’t have to remember the answer. They just have to enter the numbers in gray.
How Rocket Math corrects errors
Rocket Math, however, provides only an auditory correction. When a student answers incorrectly, the screen turns orange and Mission Control recites the correct problem and answer. In the pictured situation, Mission Control says, “Three plus 1 is four. Go again.” Under these conditions, the student has to listen to the correction and remember the answer, so they can enter it correctly.
Following an incorrect answer to a target problem, the app presents two more problems. Then it presents the previously target problem, on which the student made the error, again.
If the student answers the previously missed problem correctly within the three seconds, the game notes the error, and the student continues through the phase. If the student fails to answer the problem correctly again, the correction process repeats until the student answers correctly. Having to listen to and remember the answer, rather than just copy the answer, helps students learn better.
An effective math app gives meaningful feedback
Without feedback, students can’t learn efficiently and get frustrated. But the feedback cannot be generic. It has to dynamically respond to different student behavior.
How XtraMath’s app gives feedback
XtraMath’s charming “Mr. C” narrates all of the transitions between parts of each day’s lesson. He welcomes students, says he is happy to see them, and updates students on their progress. He gives gentle, generic feedback about how you’re getting better and to remember to try to recall the facts instead of figuring them out. However, his feedback remains the same no matter how you do. In short, it is non-contingent feedback, which may not be very meaningful to students.
How Rocket Math’s app gives feedback
Differing from XtraMath, Rocket Math offers students a lot of feedback that is contingent. Contingent feedback means that students will receive different types of feedback depending on their responses.
The Rocket Math app gives positive feedback for all the 78 accomplishments noted above. It also doles out corrective feedback when the student isn’t doing well.
As noted above, students receive corrective feedback on all errors. They get feedback when they take longer than three seconds to answer too. The “Time’s Up” screen on the right pops up and Mission Control says, “Ya’ gotta be faster! Wait. Listen for the answer.” And then the problem and the correct answer are given. Students get a chance to answer that fact again soon and redeem themselves–proving they can answer it in 3 seconds.
The app tracks errors and three strikes mean the student has to “Start Over” with that phase. At that point, the doors close (with appropriate sound effects) and then the student has to hit “go” and the doors open (with appropriate sound effects) to try it again.
When it comes to recognizing a student’s success, the Rocket Math app holds nothing back. After a student completes a phase, Mission Control gives enthusiastic congratulations as noted above.
Typically, students don’t have to “start over” more than once or twice in a phase, but they still feel a real sense of accomplishment when they do complete the phase. The feedback students get from Rocket Math matters because they have to work hard to earn it.
How much does an effective math facts app cost?
It is hard to beat the price of XtraMath, which is free. XtraMath is run by a non-profit based in Seattle. They have a staff of six folks in Seattle, and they do accept donations. Their product is great, and they are able to give it away.
Rocket Math is run by one person, Dr. Don. He supports the app, its development and himself with the proceeds. He answers his own phone and is happy to talk with teachers about math facts. The Rocket Math Online Game is a good value at $1 a year per seat (when ordering 100 or more seats). Twenty to 99 seats are $2 each. And fewer than 20 seats cost $3.89 each per year. As one principal-customer of Rocket Math said, “We used to have XtraMath. We’d rather pay a little bit for Rocket Math because the kids like it better.”
Just playing a math facts game won’t build math fact fluency
There are a lot of apps out there that look like they would help your child learn math fact fluency. If they have to answer math facts, won’t that work? Not really. Just playing a game that asks you to answer facts won’t help you learn new facts. In fact, most apps for practicing facts are discouraging to students who don’t know their facts well. Why? Because most of the people designing the app don’t have any experience teaching. A teacher, like the creator of the Rocket Math App, is trained to effectively teach new math facts (or any facts) to a student and knows an effective math app from an ineffective one.
3 essential features of an effective math fact app
There are plenty of ineffective math apps. Some apps don’t give the answers when a student doesn’t know them. Some apps just fill in the answer for the student and then move on. When the student doesn’t know the answer, the app has to teach it. To teach math fact fluency, the app has to do these three things:
The app has to tell the problem and the answer to the student.
It has to ask the student to give the correct answer to the problem.
It has to ask the problem again after a short delay to see if the student can remember the answer.
Without doing these three things there’s no way the app is going to be able to teach a new fact to the student.
An effective math app will only teach a few math facts at a time
Nobody can learn a bunch of new and similar things all at the same time. A person can only learn two, three, or four facts at a time. You cannot expect to learn more.* That’s enough for one session. The student has to practice those facts a lot of times to commit them to memory. Once or twice is not enough. It also won’t help to practice the same fact over and over. Proper math fact fluency practice intermingles new math facts along with facts the learner has already memorized. However, no more than two to four facts should be introduced at a time. If a student has to answer a lot of random untaught math facts, you will have a very frustrated learner.
Practice must focus on building math fact fluency
Some students learn to solve addition problems by counting on their fingers. That’s a good beginner strategy, but students need to get past that stage. They need to be able to simply and quickly recall the answers to math facts. An app is good for developing recall. But the app has to ask students to answer the facts quickly, faster than they can count on their fingers. The app has to distinguish when a student is recalling the fact (which is quick) from figuring out the fact (which is slow). Second, the app must repeatedly ask the learned facts in a random order, so students are recalling. But the app should not throw in new facts until all the facts are mastered and can be answered quickly.
Introduce new facts only when old facts are mastered
The trick to effectively teaching math facts is to introduce new math facts at an appropriate pace. If you wait too long to introduce math facts, it gets boring and wastes time. If you go too fast, students become confused. Before introducing new facts, students need to master everything you’ve given them. An effective app will test whether students have mastered the current batch of math facts before introducing more facts. And it will also introduce math facts at a pace based on student mastery. That’s the final piece of the puzzle to ensure students learn math facts from an app.
*Rocket Math App focuses on two facts and their reverses at a time, such as 3+4=7, 4+3=7, 3+5=8 and 5+3=8.
As a university supervisor of pre-service teachers, I’ve seen my share of bad lessons. Among the most painful were when student teachers would try to liven up their lessons to impress me by having the students do a math game. My student teachers wanted their students to learn math facts and to do so in a fun way. The picture above is typical of what I would see. Here are the reasons that most multiplication games that the student teachers implemented were awful.
Waiting for your turn at a multiplication game is not learning!
As you can see in the picture above, all but one of the students are just waiting for their turn. They aren’t doing math. The students are just watching the student who is playing. No one likes waiting, and your students are no exception. Any game that has turn-taking among more than two students wastes time.
Make sure your multiplication games are structured so all or most students are engaged and playing all the time. You want students to have as much engaging practice as possible while practicing math facts at speed. If everyone can be doing that at the same time, that’s optimal. No more than two students should be taking turns at a time.
A multiplication game that allows using a known strategy to figure out facts (like finger counting) is not learning!
Learning math facts involves memorizing these facts so that students know them by memory, by recall. Committing facts to memory is why there is a need for lots of practice. If the game allows time for students to count on their fingers or use some other strategy for figuring out the answer to facts, then there is no incentive for students to get better.
In the lower left corner of the picture you can see one student counting on their fingers—which is better than just watching—but is not learning the facts, it is just figuring them out. The most able students in an elementary school are able to memorize facts on their own when they tire of figuring them out day in and day out. But the rest of the students will just do their work patiently year after year without memorizing if you don’t create the conditions for them to memorize facts.
Make sure that your multiplication games reward remembering facts quickly rather than just figuring them out. Speed should be the main factor after accuracy. Fast-paced games are more fun and the point should be that the more facts you learn the better you’ll do.
Multiplication games that randomly present ALL the facts make learning impossible.
It is a basic fact of learning that no one can memorize a bunch of similar things all at once. To memorize information, like math facts, the learner must work on a few, two to four facts, at a time. With sufficient practice, every learner can memorize a small number of math facts. Once learners master a set of math facts, they can learn another batch. But if a whole lot are presented all at once, it is impossible for the learner to memorize them.
Make sure your multiplication games are structured so that each student is presented with only facts they know. A good game presents only a few facts at a time. As students learn some of the math facts, more can be added, but at a pace that allows the learner to keep up. The optimal learning conditions are for the learner to have a few things to learn in a sea of already mastered material.
Rocket Math Multiplication Games
We designed Rocket Math games to help kids gradually (and successfully) master math skills. Students use Rocket Math’s Worksheet Program to practice with partners, then take timings. Students can also individually develop math fact fluency—from any device, anywhere, any time of day—with Rocket Math’s Online Game.
Assign Subscriptions. The orange box on your dashboard shows the number “Unassigned Subscriptions” you have that can be assigned to students. You can give these subscriptions to students by using the blue + Import Students Logins From CSV button.
That page–the pop-up labeled “Import Student Logins From CSV” looks like this picture to the left.
Begin at #1 and click on “CSV template to fill in” to get a properly formatted starting point.
See the blank csv template to the right. You’ll enter the student’s first and last name, make up a username and a passcode for the student. Enter the code number for the learning track they will start in. You can change it at any time. Add the Teacher Mgr’s email if you wish to connect the student to a different teacher that you set up in your account.
Once you have completed the file, save it to your computer as a CSV file (it’s an excel file now, so you have to choose Save As and find Comma Separated Value -CSV in the list).
Now go back to the pop-up labeled “Import Student Logins From CSV” and do #2 Choose file and browse to the csv file you just saved and select it. Then go to the bottom of the page at #3 and hit the blue button that says “Parse CSV.”
After you hit “Parse CSV” you’ll see a list of your students. Scroll to the bottom and hit the blue button that says “Import Students.” Then they will be set up in the system.
If something goes wrong, you can use the red button on your Dashboard that says “Delete ALL students!” It is extreme, but it will clear out all of your student data, allowing you to start over and re-import.
If you have a bunch of trouble, send me your csv files and I will do the import for you. -Dr.Don