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.
Do your students struggle to complete their timed math worksheets? Is your classroom a sea of finger-counting during fast math facts practice?
Your students aren’t the problem. It’s your teaching technique that’s hindering progress.
Help your students learn math facts quickly and gain confidence in their skills with Rocket Math’s research-based program. The program works because it teaches memorization through multiple, evidence-based techniques that work for all types of learners.
Why Faster Is Better
Learning math facts at a young age plays a key role in a student’s ability to succeed throughout their education as well as out in the real world.
Not only does math fact memorization serve as a foundation to other math skills, but it also plays a part in motivating student. Most children will feel a sense of pride and excitement when they recognize their ability to quickly recall math facts.
Once a student develops instant recall, math assignments become easy and fast. It enables students to easily recognize many things about numbers that teachers call “number sense.” It gives them confidence. And frankly, they like going fast much better. This makes teaching and learning math far more enjoyable!
Fortunately, almost every child is capable of memorizing math facts in such a way that allows them to call upon them instantly and painlessly. The problem is, many traditional forms of teaching math facts are not effective.
The Problem with Traditional Teaching Techniques
When I was a teacher, I found myself frustrated with the ineffectiveness of traditional teaching tools – specifically when it came to teaching math facts. Repetition, counting, and endless worksheets seemed to leave students discouraged. These old techniques were not taking into account a few simple facts about memorization.
A More Effective Approach to Teaching Fast Math Facts
To help your students memorize math facts effectively, you need to consider five things:
How many math facts to introduce in one session
How fast a student can answer individual math facts
How fast a student can answer multiple math facts
When to introduce new math facts
How often a student practices
1. Introduce a small number of math facts in one session
In grad school, I learned a simple fact about memorization that changed the way I look at teaching math facts: the brain can only process a handful of facts at a time. This fact has shaped a foundational part of Rocket Math, the math fact program I developed to help students effectively learn their math facts.
When students are presented with too many facts – perhaps on a worksheet – the brain will not even begin to attempt remembering. Instead, it has been found that when small groups of facts are presented and practiced, the brain can easily absorb the new information.
Rocket Math uses this knowledge to help students learn much faster and gain confidence in their math skills. Rocket Math only presents two math facts and their reverse facts at a time. This simple trick makes a world of difference. As the saying goes: “How do you eat an elephant? One bite at a time . . .”.
2. Help Students Quickly Recall Individual Math Facts
There is a common misconception among teachers and parents that struggling to remember an answer is valuable. Picture the child scratching his head as he racks his brain for the right answer. Unfortunately, this is not an effective way to teach math. In order to strengthen the neural connections that are involved in memorization, recalling the correct answer quickly is key.
When students are forced to rework the problem in their head multiple times, it does nothing for their recall abilities. That is why rather than having the student guess multiple times, Rocket Math uses a correction tool that immediately reminds students of the right answer if at first, they answer either slowly or incorrectly. This helps to build the memory as they are reminded over and over of the right answer.
3. Practice a Series of Math Facts Quickly for Easy Recall
Once a child has practiced calling to mind a handful of math facts, it is time to practicing recalling them, making sure they can do so quickly. Recalling facts can be done at a high speed, whereas figuring out math facts you can’t recall can take a long time. That is why practicing fast recall is important.Repeatedly recalling fact will strengthen a student’s memory while offering a fun challenge. If the student can’t recall the math facts quickly they may need extra help from the teacher to learn the facts before continuing with quick recall practice.
Rocket Math only has students practice for a few minutes at a time, as that is all is needed when quickly recalling math facts. To measure progress, Rocket Math utilizes 2-minute timing exercises every couple of weeks to see how well students are able to recall math facts. Our free fluency tests are also a great assessment tool for testing student knowledge.
4. Carefully Build Math Fact Fluency
Teachers should be thoughtful of the rate at which they introduce new math facts. Before adding more groups of facts, previously learned facts should be well mastered. A student is ready for another handful of facts when they can recall their current set without hesitation. At first, it may seem like this approach will take longer, but because of the efficiency of memorization, students will move quickly through lessons and build math fact fluency with ease.
5. Practice Math Facts Daily for Long-Lasting Fluency
Because there are so many math facts to learn it is important to start children early and to practice daily. This gives students a chance to learn all of the math facts within all four operations. Spreading facts out over time and including daily practice throughout elementary school years will greatly improve a student’s foundational math skills.
Rocket Math: A Modern Approach to Teaching Math Facts
Rocket Math worksheets are a great way to teach math facts to children of all ages – starting as early as Kindergarten when students begin learning how to read and write numbers. The Rocket Math Universal Worksheet Program is designed for daily practice in order to build a solid foundation of basic math skills.
Our Universal Worksheet Program follows a simple structure and routine to help students progress at an appropriate rate throughout their different grade levels. Throughout the sequence, students learn all of the building blocks necessary to succeed throughout elementary and middle school.
If you have students that are behind for their grade level, our worksheet program makes it easy for you to revisit previous lessons that will reinforce the concepts that are necessary to move forward. Likewise, there are plenty of supplemental worksheets within the program to keep advanced students engaged.
Kindergarten Math Worksheets
The first math-related goal for Kindergarteners should be to learn how to write numerals. It is important for children to learn the most efficient way to write numerals. Think about it – how do you write the number eight? Where does your pen begin on the page?
Believe it or not, this is something that is learned and becomes second nature. This skill is important to develop early on as the first building block to learning math.
If children in first grade cannot write numerals legibly and efficiently, they should begin the year with Rocket Writing for Numerals. Once they understand the concept of addition, first graders are ready to begin memorizing addition facts.
The Rocket Math Worksheet Program includes Addition 1s through 9s. Students work through 26 levels (A to Z) learning two facts and their reverses on each level. They practice orally for 2 minutes with a partner who corrects any hesitations or errors.
Alternatively, once students have learned the concepts for both addition and subtraction, they can begin to learn Fact Families. Our Fact Families 1 to 10 Add and Subtract worksheet program begins teaching fact families. Set D of this worksheet to the right is an example, teaching four related math facts such as 3+2, 2+3, 5-2, and 5-3.
Common Core suggests that students be fluent with addition facts up to 20, such as 13+6=19. Personally, I think if a student knows 3+6=9, they don’t need to practice 13+6. However, Rocket Math has made available a program for these facts, Add to 20 in the Universal subscription.
Rocket Math makes it easy for teachers, as the consistent structure provides an easy daily routine for students in all programs and levels. Because the Rocket Math Worksheet program follows a sequence and routine, it is easy for students to continue working together even when studying different programs or levels.
2nd Grade Math Worksheets
Upon starting second grade, students should have mastered all of their addition facts, or fact families 1 to 10. If they have not mastered those facts, you should begin with the first-grade worksheets (Addition 1s through 9s/Fact Families 1 to 10 Add and Subtract) until they are ready to move forward.
The goal for second graders is to learn subtraction (and addition facts) by the end of the year. Rocket Math has a Worksheet Program for Subtraction 1s through 9s that is perfect for second grade. If students master the subtraction facts through practicing with Rocket Math they will be able to learn the lessons of re-grouping, a.k.a “borrowing”, much more easily.
If students have been using the Fact Families Program, it is best to continue using that sequence. Second graders should be ready for Fact Families 11 to 18 Add & Subtract. The last ten levels of this program review all the fact families so that students will be quite solid in their mastery by the time they reach Level Z.
For second-grade students who have mastered addition and subtraction facts, skip counting is a great next step. Skip counting is easy and fun for students while preparing them for multiplication in third grade.
Rocket Math’s Skip Counting program is a uniquely designed worksheet. When students are practicing together, the checker has to rotate the paper to keep up as the other is quickly skip counting.
Because of that, students especially enjoy this worksheet. Not to mention, the design incorporated playful Rocket graphics, which causes it to resemble a game rather than a math worksheet!
Common Core suggests that students be fluent with subtraction facts up to 20, such as 19-6=13. Personally, I think if a student knows 9-6=3, they don’t need to practice 19-6. However, Rocket Math has made available a program, Subtract from 20, so students can practice these facts.
3rd Grade Math Worksheets
The priority for third grade is to learn multiplication. Textbooks begin teaching the concept of multiplication from very early in 3rd grade. Your goal should be to introduce multiplication facts by the time the textbook is giving students multiplication problems to solve.
Using the Rocket Math Skip Counting worksheet can help ease students into learning multiplication facts. If possible the Skip Counting worksheet should be used before students are asked to start performing a lot of multiplication.
The first step to successfully teaching multiplication facts is teaching memorization. The Rocket Math Multiplication 1s to 9s is designed to build strong multiplication fact fluency and recall. This technique avoids the problem of students having to look up facts in times tables, over and over again.
Achieving mastery in multiplication facts is the only way for students to keep up in math throughout elementary and middle school. Even if students come to you without having a solid foundation of addition and subtraction, it is crucial that you teach mastery in multiplication.
For quick-learning students, who get through Multiplication 1s through 9s before the end of the year, a good supplemental Worksheet Program is Multiplication 10s, 11s, 12s. Building upon the facts from Multiplication 1s to 9s, students progress easily through this next set of facts. And of course, students consider it a badge of honor to be members of the “tens, elevens, and twelves” club!
4th Grade Math Worksheets
By the end of fourth grade, students should have learned all four basic operations of math facts. Fourth graders should be using then Division 1s through 9s worksheet to learn division facts.
While division facts are derived from multiplication, it is very valuable for students to explicitly learn the division facts. Long division comes much easier for students who have learned division facts.
For students who get all the way through Level Z in basic division, there is a supplemental program: Division 10s, 11s, 12s. It builds upon and reviews facts from Division 1s to 9s while keeping learning fun for students who work faster.
Math Worksheets for 5th grade and up
Students who have been learning math facts since kindergarten have built a great foundation by the time they reach fifth grade. Unfortunately, this is not the case for many students, which makes it difficult for teachers to create lessons suitable for everyone’s level.
Rocket Math provides an easy solution for these teachers. Simply take ten minutes a day utilizing the worksheet program to teach the four basic operations. While these students are catching up, the remaining students can do Rocket Math as well!
We offer five programs that teach more advanced math skills that follow the same structure and routine. Each one of these five different programs includes video lessons that teach students both how to use the program and how to do the skill that is being introduced.
Uses the vertical number line to show how these work.
5) Mixed Integers (adding and subtracting positive and negative numbers)
Uses the same vertical number lines but now mixes the 8 types of problems together.
Rocket Math’s goal is to make learning fun for everyone – students and teachers. By following the worksheet program, even students who have struggled in the past can begin gaining confidence in their math skills.
Testing season is stressful. The task of scheduling testing for each student in the school is difficult. It causes significant stress due to time logistics, student absences, and disrupted schedules. Teachers know how difficult it can be to deal with odd and awkward time gaps. What testing season activities can fill those holes?
Teachers spend a lot of time juggling schedule and testing material. Students are anxious about the tests as well. Often the mood in the classroom can feel tense.
We at Rocket Math are concerned about the success of students. We know how precious teaching time is. We believe that doing Rocket Math practice sessions can significantly aid during the busy spring test season. Here are five reasons why doing Rocket Math is a great activity during testing season.
1. Rocket Math is a time efficient testing season activity.
Your students are familiar with the Rocket Math routine. They know just what to do. The process of doing Rocket Math from start to finish should take no longer than ten to fifteen minutes. When you have one of those short intervals created by the testing schedule, you can make good use of this short amount of time. Rocket Math fits in a short amount of time and is still productive.
2. Rocket Math can be used during multiple testing season gaps.
As test schedules tend to have multiple gaps, Rocket Math works great as an activity that can be used multiple times throughout the day without causing extra work for teachers. Students actually appreciate the opportunity to have another chance to practice Rocket Math in the same day.
Students can easily use Rocket Math a second or third time during their school day without any negative impact. In fact, multiple sessions of Rocket Math during a single day can help students progress faster.
3. Rocket Math is a testing season activity that doesn’t require re-teaching lessons.
As students are taking make-up tests, the rest of their classmates need something to do in the classroom. Because students work in pairs during Rocket Math allows students to work through math lessons on their own. Because it is just practice, there is no need to re-teach material, students taking their make up tests filter back into the classroom.
As long as there is at least a 15-minute gap between testing sessions, students can easily complete a Rocket Math session. The best part is, because students are familiar with the Rocket Math process, teachers don’t need to explain a new activity to each student who filters in after testing.
4. Rocket Math is a highly engaging and productive testing season activity.
Many teachers struggle to fill time in the gaps between test sessions. Reading time or make-up work is often the go-to solution. Teachers know that these activities don’t seem productive or engaging. Plus, students know that these time-filling activities “don’t count.” Rocket Math however, does count!
5. Rocket Math is a testing season activity that students truly enjoy.
Accountability tests can cause stress due to unfamiliarity, whereas Rocket Math offers students comfort in an activity that they know and enjoy. As Rocket Math shows progress along the way, each student gains a sense of pride in their accomplishment and is more likely to feel motivated to continue learning.
When there are gaps between test sessions, Rocket Math can provide students a boost of confidence as they are instantly gratified by their success.
During this busy spring test time, I highly recommend teachers are prepared with their Rocket Math folders to help productively fill the time gaps left in the daily schedule. Rocket Math is a quick and easy testing season activity. It can be used during multiple gaps as an engaging learning tool. Doing Rocket Math helps students feel accomplished in an otherwise stressful testing period.
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?
Basic, Optional, and Alternative—there are a lot of different Rocket Math programs. But which program should you use first? And in what order should you teach fast math facts? Well, it all depends on the grade you teach and the fast math facts your students have already memorized.
An overview of Rocket Math’s fast math fact programs
Rocket Math offers multiple programs because their are several ways to teach fast math facts.
The Basic Program
Rocket Math’s basic program includes Addition, Subtraction, Multiplication, and Division (1s-9s). The basic program must be mastered by all students.
The Alternative Program: Fact Families
There is another way to learn facts, which is called Fact Family math. Instead of learning all Addition facts, students can learn Addition and Subtraction facts at the same time. A fact family consists of four related facts, for example: 3+2 = 5, 2 + 3 = 5, 5 – 3 = 2, 5 – 2 = 3. As an alternative to using the Basic Program, students can learn fact families up to 10 in first grade. Then students can move on to the upper fact families 11 to 18 in second grade. There is no clear evidence that this way is better or the separate operations way is better. That’s why we offer both options.
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 Kindergarteners 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:
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.”
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.