Say, “The game is always right. Just do the problem over again.”
Teachers write saying their students complain that the Online Game said they were wrong, when they were right. This is similar to a problem we found with students and their checkers in the Worksheet Program. Bear with me a second while I explain.
In the Worksheet Program students often complain to their teacher that their checker made them do the problem over, even though they weren’t wrong. Trying to adjudicate such a dispute is nearly impossible, as veteran teachers have learned the hard way. The extra practice didn’t hurt the students and you’re going to be inundated with complaints if you try to adjudicate them. In workshops we always counseled teachers to respond to such complaints with, “The checker is always right. Just do the problem over again.”
The extra practice that the Online Game) makes a student do is never harmful. The problem and the answer that Mission Control gives is never wrong. When students complain to you about the game telling them a right answer was wrong, just tell the student, “The game is always right. Just do the problem over again.”
The Online Game only says right answers, so it’s not wrong.
The correction procedure says both the problem and the correct answer. Students may say, “But, that’s what I put!” They are not confused. They are just complaining that they were “unjustly” corrected. An unjust correction is relatively unimportant compared to an actual error.
The program never says a student’s answer is “wrong.” The game does a correction whenever it does not process the correct answer within the time limit. The student may hit the correct answer just a fraction of a second too late to be processed by the game. Even though correct, the game will say “Time’s Up” and do a correction.
Sometimes a student misses the button they mean to hit, they make a “typo,” and the game buzzes and the screen shakes “no.” Sometimes, a glitch occurs and it skips ahead to the next problem and processes the last answer as incorrect. However, the game can only say a problem and its correct answer as those are the only words that are recorded. There are no recorded errors. For example the game will say, “Six plus two equals eight. Go again.” After that the game waits for the student to enter the correct answer AND waits for the student to hit the checkmark. No amount of arguing, “But that is what I put!” or “But that wasn’t the problem I was answering” will change it.
The extra practice caused by an “unjust correction” is not harmful.
Students should listen to Mission Control while it is displaying and saying a problem and the correct answer. Then they will know what they should do. They should just enter the answer and hit the checkmark. Students should just do the problem over again regardless of whether or not they think they entered the right answer. The game never says anything incorrect and the extra practice won’t hurt them. While an unjust red “X” for an error seems terrible to students, it will not do anything other than give them more practice, which is good for them.
We offer a $50 gift certificate to the store of your choice if you can capture an error by the game on video, as we have never seen the game make an error and can’t replicate the problem.
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.
Students counting on their fingers is a sure-tell sign that they didn’t acquire math fact fluency. It is sad to see students, ashamed of the only thing they know, counting on their fingers under their desks. Our elementary educational mission is failing students who haven’t developed math fact fluency, which is the foundation to more advanced math skills.
Developing math fact fluency takes structure, organization, and work on the part of both teachers and students. In this article, I will share everything you need to know about developing math fact fluency.
What is Math Fact Fluency
Math facts are single-digit problems such as 7+9 or 6×8 or 14-5, and so on. A common name for all the multiplication math facts is the “multiplication table.” Math fact fluency is the ability to answer all math fact questions instantly from recall without having to think through the problem.
Students should be able to recall math facts instantly without having to count on their fingers or hesitate to think about the answer. This may seem like a high bar, but our brains are great at recalling an unbelievable amount of information daily, and with practice, math facts can be recalled the same way.
Three Reasons Why Math Fact Fluency is Important
Math fact fluency is critical because it is a “tool skill.” Meaning, it is a tool that is used in the process of doing other math problems. Developing this tool skill makes learning math easier as concepts get more complicated. This tool skill needs to be automatic in the student’s brain, in order to save precious short-term memory resources.
Math fact fluency can be compared to reading. Students must recognize words automatically to comprehend the author’s meaning. Otherwise, they will spend too much time decoding individual words.
When students are fluent in math facts, they are focused on the math process as a whole, rather than stopping to puzzle out the facts. This is important for three reasons:
1. Students with math fact fluency make fewer errors
Students who lack math fact fluency often make careless errors doing arithmetic computations . If they devote too much energy to deriving math facts, they lose sight of the problem at hand and make mistakes that would otherwise be obvious. Those who can effortlessly recall math facts can concentrate on what they are doing, and ultimately make fewer errors.
2. Math fact fluency makes learning math easier
When a new math procedure is introduced, students who have math fact fluency can easily follow the thread of instruction. Without this fluency, students fall behind instruction or demonstrations as they try working out math facts. This distraction takes away from a student absorbing all of the details necessary to successfully learn new math processes.
The first teacher to use Rocket Math to teach subtraction facts to her second graders realized the benefit first hand. She told me that with Rocket Math, she was able to teach regrouping in subtraction in just three days.
Her students mastered the math facts, and the outcome was extraordinary. The teacher shared that since these students had developed fluency in subtraction facts, they were able to learn other procedures easily.
3. Students who have developed math fact fluency enjoy math and always complete their work
Having to count on your fingers or look up facts on a timetable is slow and onerous. When students can’t work quickly, math problems become a dreaded drudgery. Students are motivated by mastering new skills, which will help them work faster and build confidence . Those who can quickly recall math facts will complete their work with ease , and enjoy the feeling of accomplishment.
How to Build and Improve Math Fact Fluency
Building and improving math fact fluency requires a systematic effort over the elementary years. It is a long climb to achieve mastery and there are no short-cuts.
Consistent daily practice throughout elementary school is important for retention. Slow and steady wins the race when building math fact fluency.
Math fact practice should be structured in such a way that students are learning a small number of facts at a time. These small groups of facts should be practiced daily until students have reached mastery. As time goes on, more groups of math facts are introduced systematically in small amounts for students to master.
Learning 1s to 9s facts in the four basic operations will take elementary students months to master. Worksheets and game applications are two of the best ways to teach math fact fluency over time. Combining structured math fact learning, practice, and evaluation with fun math fact games helps students develop number sense and understand complex numerical relationships.
Teaching Math Fact Fluency with Worksheets
Worksheets are popular tools that teachers reach for when teaching math facts, but sadly, they often fall short for the majority of students. A few select students will begin memorizing the facts on their own accord in order to make the worksheets easier, but most students will continue to slowly work out the facts either on their fingers or in their heads. These students may never develop a strong recall of the facts and become flustered when asked to answer problems on the spot.
Fortunately, there are specific worksheets that are effective in building math fact fluency. The key is having worksheets that are structured, systematic, and sequenced. Each worksheet should only have two to four facts to be learned.
By working on only two to four facts, these worksheets help teach memorization for a strong recall, rather than reinforcing working out problems slowly. Students will then be able to remember these small groups of facts easier, and by the end of the worksheet will be writing answers from memory.
Teaching Math Fact Fluency with The Rocket Math Worksheet Program
TheRocket Math Worksheet Program improves upon this concept by using paired practice and saying facts aloud. Students partner up and practice quickly recalling facts together. One student asks the questions and watches for when their partner hesitates to answer. He or she then gives his or her partner more opportunities to practice the harder facts.
The students switch roles, and after both have answered questions, they then take a one minute test on the facts that they have learned so far. If students are answering as fast as their fingers will carry them, then they pass the level and move on to the next worksheet in the sequence.
Ten minutes of practice every day gets the job done, especially when paired with using these facts in higher level math problems.
Teaching Math Fact Fluency with Games
In addition to worksheets, schools of education tell teachers to use games to “teach” math facts. Unfortunately, most games and fun activities do not actually help individual students learning math facts to the level of fluency. These games, such as bingo or dice, have several fallouts:
– Students spend most of their time waiting for their turn rather than practicing facts.
– They do not focus on teaching a small group of facts in a manner that helps students commit them to memory.
– The games do not adjust to an individual student’s level of fluency.
– Students can pace the game slowly enough to have time to figure out facts rather than requiring recall.
– It is difficult to keep every student engaged, as those who are behind are less likely to participate.
Using the Rocket Math Online Game as an Effective Way to Teach Math Fact Fluency
There are games that are very effective at building math fact fluency. Games such as theRocket Math Online Game have several important features that make a big difference.
Every student is engaged in answering math facts—not waiting for a turn.
Students learn only a few new facts at a time so that they can remember them.
The game provides lots of focused practice on each set of facts.
The game requires students to answer quickly, which guarantees the students recall the answer rather than “figuring it out” over and over.
The game gives an immediate correction and extra practice on any facts that students cannot answer quickly and correctly.
The game only introduces new facts once students demonstrate mastery of facts learned so far.
The game gives students explicit feedback so they have a sense of accomplishment as they work their way through an operation.
Math Fact Fluency Benchmarks
The following benchmarks are reasonable expectations for a school that has an effective math fluency program in place. Of course, a student cannot write math facts any faster than they can normally write, so take that into account when looking at fluency benchmarks. Adjust the benchmarks for students who do not write quickly.
Rocket Math’s assessment packet includes a writing speed test, which helps create realistic expectations for individual students. Using the goal sheet ensures you will evaluate the individual student math fact fluency in light of their writing speed.
Rate students as:
Weak, needs fact work
Good, but fact work could help
Strong, fact work not needed
Special triage priority: if you have fourth-grade students and above, start with multiplication facts. Multiplication facts are essential to future success in math above fourth grade. Even if fourth graders are counting on their fingers for addition and subtraction, teach multiplication mastery first. If fourth graders move to the next grade without strong multiplication fact fluency, they will have a hard time successfully progressing through math.
The Best Tools for Developing Math Fact Fluency
With the right tools, any student can develop math fact fluency and have fun while doing it! Students use Rocket Math’s Subscription Worksheet Program to practice with partners, then take timed tests. Rocket Math also offers math facts practice online through the Rocket Math Online Game. Students can log in and play from any device, anywhere, any time of day! Start a free trial today.
Both the worksheet program and the online game help students master addition, subtraction, multiplication, and division math facts for a lifetime of success in math.
Dr. Don has created another math program and put it into the Universal level virtual filing cabinet at Rocket Math. This is a beginning program for kindergarten students. That means they can’t learn on their own, the teacher must provide instruction. Teachers can use the worksheets to effectively teach students to count objects aloud and then match the word with the numeral. You can see the top half of Worksheet A here.
I do–demonstration of counting.
Each worksheet begins with a demonstration of counting objects and circling the numeral that matches. On Worksheet A there are only the numerals two and three to learn. The teacher demonstrates (best with a document camera so all students can see) how she counts the objects and then points out that the answer is circled. Suggested teaching language is something like this,
“I can do these. Watch me count the frogs. One, two, three. There are three frogs in this box. So they circled the three. Everybody, touch here where the three is circled. Good. How many frogs were in this box, everybody? Yes, three. Now watch me do the next box.”
We do–counting together.
In the “We do” portion of the worksheet the teacher counts the stars first as a demo and then with the students. Worksheet A you all just count 3 stars. Suggested teaching language is something like this:
“Our ‘We Do’ says to touch and count. Start at zero and count each star. We are going to touch and count the stars. Put your counting finger on zero, everybody. We are going to start at zero and count each star. Let’s count. One, two, three. We counted three stars. That was great! Let’s do it again! Fingers on zero, everybody. Let’s count. One…”
By Worksheet S the teacher and the students are counting 12 stars together.
The program has a page of teacher directions, with suggested language for teaching the worksheets.
You do–independent counting.
In the “You do” portion of the worksheet (after learning the numerals with the teacher), the students are asked to count the items in each box and circle the correct number. They are not asked to form the numerals–that’s numeral writing skill. They just identify the numeral and circle it. Besides cute items there are also dice to count, fingers to count and hash marks to count–so students can learn multiple ways of keeping track of numbers.
Passing a level requires 100% accuracy. Students who make any errors should be worked with until they can complete the worksheet independently and get all the items correct.
This Beginning numerals program will build strong beginning math skills for kindergarten students learning the meaning of numerals. Combined with Rocket Writing for Numerals it will set students up for success in elementary math.
Basic, Optional, and Alternative—there are a lot of different Rocket Math programs. But which program should you use first? And in what order should you teach fast math facts? Well, it all depends on the grade you teach and the fast math facts your students have already memorized.
An overview of Rocket Math’s fast math fact programs
Rocket Math’s basic program includes Addition, Subtraction, Multiplication, and Division (1s-9s). The basic program must be mastered by all students.
The Alternative Program: Fact Families
There is another way to learn facts, which is called Fact Family math. Instead of learning all Addition facts, students can learn Addition and Subtraction facts at the same time. A fact family consists of four related facts, for example: 3+2 = 5, 2 + 3 = 5, 5 – 3 = 2, 5 – 2 = 3. As an alternative to using the Basic Program, students can learn fact families up to 10 in first grade. Then students can move on to the upper fact families 11 to 18 in second grade. There is no clear evidence that this way is better or the separate operations way is better. That’s why we offer both options.
The rest of the fast math facts programs like Rocket Writing for Numerals or Skip Counting are optional. You should only offer these programs to students once they have memorized the fast math facts through the Basic Program or the Alternative Program.
The only exception would be in a school where Kindergarten students did not get a chance to learn how to quickly and easily write numerals. In that case, you might take the first two months of the first grade year to run students through Rocket Writing for Numerals before beginning Addition (1s-9s).
Let’s take a closer look at how to implement each program in different grade levels.
First grade math facts: Learn Addition
Rocket Math fast math facts programs for first graders include:
The Basic Program
The Alternative Program
Fact Families (1-10) Add & Subtract
Rocket Writing for Numerals
Add to 20
If first grade students are taking all year to get through sets A-Z in Addition in the Basic Program, they need some extra help. You should intervene to help students who take more than a week to pass a level. Often they need to practice better or practice with a better partner. Some may need to practice a second time during the day or at home in the evening. First grade students who finish the 1s-9s can move on to the Add to 20 Optional Program for the remainder of the year.
Likewise, if you choose to teach Fact Families (1-10) Add & Subtract from the Alternative Program instead of using the Basic Program, your students can use the Optional Programs for supplemental learning purposes.
Second grade math facts: Learn Addition and Subtraction
Rocket Math fast math facts programs for second graders include:
The Basic Program
The Alternative Program
Fact Families (1-10) Add & Subtract
Fact Families Part Two (11-18) Add & Subtract
Subtract from 20
Second grade students must have completed Addition before starting on Subtraction (1s-9s). They can also test out of Addition through the Placement Probes. Second graders who cannot test out of Addition in first grade or didn’t complete it in first grade must focus on Addition. Only after getting through Set Z of Addition should they move into Subtraction.
You can substitute the Basic Program’s (1s-9s) Addition and (1s-9s) Subtraction for the Alternative Program’s Fact Families (1-10) Add & Subtract and Fact Families Part Two (11-18) Add & Subtract.
Second grade students who complete Addition and Subtraction 1s-9s (or the Alternative Program) can move on to Subtract from 20. Students who finish Subtract from 20 can do Skip Counting, which does a great job of preparing students to learn Multiplication facts.
Third grade math facts: Learn Multiplication
There aren’t any Alternative Programs available for third graders from Rocket Math. There are only Basic and Optional Programs. These include:
The Basic Program
(1s-9s) Multiplication (priority)
10s, 11s, 12s Multiplication
In third grade, Multiplication has priority—even if students have not mastered Addition and Subtraction. Multiplication facts are so integral to the rest of higher math that students are even more crippled without Multiplication facts than they are having to count Addition and Subtraction problems on their fingers. So do Multiplication first. Then, if there’s time, students who need to do so can go back and master Addition and Subtraction. Once all three of these basic operations are under their belts, students can go on to 10s, 11s, 12s in Multiplication (one of the Optional Programs). If students successfully progress through each program and there is enough time left in the school year, introduce the Factors program next.
Fourth grade math facts: Learn Multiplication and Division
Like the programs for third graders, there aren’t any Alternative Programs available for fourth graders. There are only Basic and Optional Programs, which include:
The Basic Program
(1s-9s) Multiplication (priority)
(1s-9s) Division (second priority)
10s, 11s, 12s Multiplication
In fourth grade, students need to have completed Multiplication before going on to Division. If they complete Division, they can go on to 10s, 11s, 12s Division, followed by Factors, and then equivalent fractions (shown in the fifth grade section below).
Fifth grade math facts: Learn all basic operations first, then they can branch out
By fifth grade, students should have completed all four basic operations (1s-9s) within the Basic Program (or the Alternative Program for grades one and two). If students have not completed these basics (and cannot test out of them with the Placement Probes) then the sequence they should follow is Multiplication, followed by Division, then go back and complete Addition followed by Subtraction. The same recommendations hold for students in any grade after fifth.
Once students have mastered the basics (1s-9s add, subtract, multiply, divide), the supplemental pre-algebra programs are recommended. These will help more than learning the 10s, 11s, 12s facts. I would recommend this order:
Math Fluency Programs should be part of on-going elementary school routines
Most elementary teachers do some activities to promote math fluency. Yet many elementary children are not fluent with math facts by the time they hit upper elementary or middle school. A hit-or-miss approach allows too many students, especially the most vulnerable, to slip through the cracks. Math fluency programs, like Rocket Math’s Worksheet Program, need to be part of your elementary school’s routine. Effective math fluency programs should be properly structured and every math teacher should be on board, every year.
Math fact fluency enables students to develop number sense
Many teachers learn in their training programs about the importance of “number sense.” Students who have “number sense” can easily and flexibly understand relations between numbers. They can recombine numbers in various ways and see the components of numbers. Students with number sense can intuit the fact that addition and subtraction are different ways of looking at the same relations.
What is not taught in most schools of education is that developing fluency with the basic math facts ENABLES the development of number sense much better than anything else. Once students memorize facts, they are available for students to call upon to understand alternate configurations of numbers. Students find it much easier to see the various combinations when they when they can easily recall math facts. Once students master the basic facts, math games that give flexibility to thinking about numbers become much easier.
It may be hard for new teachers, straight from indoctrination in the schools of education, to imagine this is true. However, if they land in an elementary school with a strong math fact fluency program they will see the beneficial effect of memorization.
Why is math fact fluency important
In the primary grades, students who have not developed fluency in math facts will have a harder time learning basic computation.
Students who are not fluent with math facts find the worksheets in the primary grades to be laborious work. They finish fewer of them and may begin to dislike math for this reason.
By the time students reach upper elementary, if they have not memorized the math facts, they find it very difficult to complete math assignments at their grade level. They find themselves unable to estimate or do mental math for problem-solving. The need to figure out math facts will continue to distract non-fluent students while they are learning new math procedures like algorithms.
In the upper grades, their inability to figure out multiplication facts becomes a huge stumbling block. Manipulations of fractions, decimals, and percentages will not make intuitive sense to students because they haven’t memorized those facts. Without math fact fluency, students rarely succeed in pre-algebra and may be prevented from learning algebra and college-level math entirely.
Math fact fluency must be assured through regular monitoring
Some students will need up to ten times more practice to develop math fluency than other students. Therefore, monitoring student success in memorizing the facts is critical. Teachers can assume that what is “enough practice” for some students is NOT going to be enough practice for all students. Effective math fluency programs must have a progress monitoring component built in. Progress monitoring gives comparable timed tests of all the facts at intervals during the year. Teachers look at the results of these timed tests to check on two things:
1. Are students gradually improving their fluency with all the facts gradually over the year?
In other words, are students able to answer more facts in the same amount of time? If they aren’t improving, then the instructional procedures aren’t working and need to be modified or replaced. Math fluency programs like Rocket Math’s Worksheet Program have two minute timings of all the facts in each operation that can be given and the results graphed to see if there is steady improvement.
2. Are all students reaching expected levels of performance at each grade level each year?
Proper math fluency programs identify students who are not meeting expectations and give them more intensive interventions. Ultimately, by the end of fourth grade all students should be able to fluently answer basic 1s – 9s fact problems from memory in the four operations of add, subtract, multiply and divide. Fluent performance is generally assumed to be 40 problems per minute, unless students cannot write that quickly.
Expectations vary by grade level and the sequence with which schools teach facts can vary. While it is great to achieve all that the Common Core suggests, it is critical only to assure that students master and gain fluency in 1s through 9s facts. Some schools in some neighborhoods may find that waiting until second grade to begin math facts may not provide enough time for all students to achieve fluency. When to begin fact fluency and how much to expect each year should be based on experience rather than some outside dictates.
Successful math fluency programs must have these 3 features
Sequences of small sets
No one can memorize ten similar things, like the 2s facts, all at once. Students easily master math facts when they can learn and memorize small amounts of facts at one time. Effective math fluency programs define math fact sequences, which students memorize at their pace before moving onto new math facts. Rocket Math’s fluency program uses only two facts and their reverses in each set from A through Z.
Even if you only introduce small sets of math facts, some students need more time to memorize than others. If you introduce the facts too fast, students will begin to jumble them together and progress will be lost. The pace of introducing facts must be based on mastery—not some pre-defined pace. This is why doing all the multiplication facts as a class in the first six weeks of third grade does not work. It is just too fast for some students. Once they fall behind it all becomes a blur.
Effective practice and corrections
When students are practicing facts, they will come to ones they have forgotten or can’t recall immediately. Those are the facts on which they need more practice. Allowing students to stop and figure out the facts they don’t know while practicing, does not help the student commit them to memory. Instead, students need to IMMEDIATELY receive the fact and the answer, repeat it and try to remember it. Then they need to attempt that fact again in a few seconds, after doing another couple of problems. If they have remembered the fact and can recall it, then they are on their way to fluency. But students must practice the next day to cement in that learning.
Math fluency programs like Rocket Math’s Worksheet Program teach students math facts in small sets, allow students to progress at their own pace, and support effective practice and error correction. Each Rocket Math Worksheet program has 26 (A to Z) worksheets specially designed to help kids gradually (and successfully) master math skills. Gain access to all of them with a Universal Subscription or just the four basics (add, subtract, multiply, divide–1s to 9s) with a Basic Subscription.
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.
Teachers do NOT need to grade, score, or check daily Rocket Math 1-minute math fluency practice tests unless the student has met their goal. Students do NOT need to grade their own daily Rocket Math fact fluency tests either.
Why grading each math test is not important
The important part of math fluency practice is the oral practice with the partner before the test–what’s going on in this picture. Because the students are orally practicing every day and getting corrections from their partners, there should be VERY FEW errors on the 1-minute math fluency written tests.
Correcting written tests doesn’t help students learn anyway. Corrections are only helpful if they are immediate, the student has to acknowledge the correct answer, and remember it for a few seconds–all of which is part of the oral correction procedure. “Correcting” what’s on the paper takes a lot of time and does not help students learn more, so it shouldn’t be done. But you have to check them before declaring that the student has passed a level.
How do you know if a student passes?
Students should have a packet of 6 sheets math fact fluency sheets at their level. Each Rocket Math student has an individual goal. For example, if a student has a goal of 32 (based on their Writing Speed Test) and they only do 31, they know they did not pass. If the student does 32 or more, they pass!
What to do when a student beats their goal (passes)
If a student meets or beats their goal, then have them stand up, take a bow, and then turn their folder into a place where you check to see that all problems were answered correctly. When YOU check (after school?), make sure all of the completed problems were correct and the student met their goal. If so, then you put the unused sheets in that packet back into the filing crate and re-fill the student’s folder with a packet of 6 worksheets at the next level and hand the folder back the next day.
When students receive the new packet of worksheets, they know to color in another letter on the Rocket Chart (and maybe put a star on the Wall Chart).
What to do if a student doesn’t pass?
Students who don’t meet their goals, don’t pass. These students should put the non-passing sheet into their backpacks and take the sheet home for more practice.
The next day they will use the next sheet in their packet of 6. If you want to give them points, do that the next day after they bring back their worksheet where they did a session at home (signature of helper should be there) and all items on the test are completed. If that’s done, they get full points.
Sometimes you’ll catch errors on sheets that students turn in as “passes.” If you see an error, the student doesn’t pass. As a result, the student keeps the old packet and has to continue with that same level worksheet.
Once students know the procedure, they should stop counting and memorize!
When it comes to math facts like 9 plus 7 or 8 times 6 there are only two things to know. 1) A procedure to figure it out, which shows that you understand the “concept.” 2) What’s the answer?
It is important for students to understand the concept and to have a reliable procedure to figure out the answer to a math fact. But there is no need for them to be required to use the laborious counting process over and over and over again! Really, if you think about it, even though this student is doing his math “work” he is not learning anything.
Math teaching strategy: Go ahead and memorize those facts.
(It won’t hurt them a bit. They’ll like it actually.)
Once students know the procedure for figuring out a basic fact, then they should stop figuring it out and just memorize the answer. Unlike capitals and countries in the world, math facts are never going to change. Once you memorize that 9 plus 7 is 16, it’s good for a lifetime. Memorizing math facts makes doing arithmetic MUCH easier and faster. Hence our tagline
Rocket Math: Because going fast is more fun!
Memorizing facts is the lowest level of learning. It’s as easy as it gets. But memorizing ALL the facts, which are similar, is kind of a long slog. Some kids just naturally absorb the facts and memorize them.
Math teaching strategy: Find a systematic way for students to memorize.
A lot of students don’t learn the facts and keep counting them out over and over again. They just need a systematic way of learning the facts. Students need to spend as much time as necessary on each small set of facts to get them fully mastered. If the facts are introduced too fast, they start to get confused, and it all breaks down. Each student should learn at their own pace and learn each set of facts until it is automatic–answered without hesitation and without having to think about it. This can be accomplished by everyone, if practice is carefully and systematically set up. It should be done, because the rest of math is either hard or easy depending on knowing those facts. And don’t get me started about why equivalent fractions are hard!