Help your kid get fast at math facts

Your kid wants to go fast at math.

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

The usual kind of practice will not make them fast.

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

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

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

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

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

Practicing math facts fast requires recalling them.

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

Cumulatively adding more facts needs to be done carefully

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

Practicing fast math facts needs to be daily

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

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

Improving math achievement: what’s unique about Rocket Math?

Rocket Math is dedicated to improving math achievement. Long-time educator Dr. Don Crawford founded Rocket Math because of his passion for effective educational tools. He believes all students can succeed in math and dedicated his company to making it happen. Their achievement and success motivate students more than anything else. Rocket Math’s mission is to help students succeed in math.

Motivated by success.

Rocket Math’s Online Game educational app teaches and develops fluency in basic math facts. The app is unique in a couple of respects. First, the game focuses students on their progress in learning math facts rather than distracting them with a cutesy game format. As students fill in their individual Rocket Chart, they become motivated by their progress in learning the facts and developing fluency. Moreover, they also develop confidence and improved self-esteem as a by-product of the process.

Evidence of effectiveness in teaching.

Second, the rocketmath.com website uniquely provides real-time evidence of its effectiveness. Rocket Math charts all its users, showing they are learning and developing fluency with basic math facts. Go to their Evidence of Effectiveness page, and you can see students’ results on fluency tests. The tests are given four times in each learning track (pre-test, 1/3 through, 2/3 through, and post-test). For example, over 55,000 students have completed the Multiplication learning track. The chart shows they began with an average fluency of 11 problems per minute at the pre-test. Those students finished the Multiplication Learning Track with an average of 21 problems per minute. Student scores show they are more fluent at each milestone in all 16 learning tracks, from beginning Addition to Fraction and Decimal Equivalents.

The most powerful thing you can do to improve math achievement.

Helping students develop fluency with basic math facts is the single, most powerful thing school administrators can do to improve student math achievement. There’s no excuse for allowing students to struggle and count on their fingers or rely on multiplication charts while trying to do math. Rocket Math has the mission of fixing that for anyone who uses their app. They even offer a 30-day initial, complimentary subscription so you can see that it works before paying a dime. Rocket Math has a money-back guarantee that using their app will improve student fluency in math facts. Rocket Math continues to grow thanks to the enthusiasm of its customers.

Things-to-look-for (any time of day) for Rocket Math implementation

Evaluating a Rocket Math implementation when you aren’t observing Rocket Math in action.

Most of the time when you go into classrooms, something other than Rocket Math® will be going on. These are the things you can check on even when there are no students in the room. There are eight indicators you can see by looking at student folders.  There are four indicators while looking at the Rocket Math filing crate.  There are additional indicators to look for if there is a Wall Chart being used or if there are Race for the Stars games in the room.  Here’s a link to the checklist.

Look at several Student Folders

(1). Students all have folders that appear to be used daily. The folders are the heart of the organizational system. Students should keep their materials in the folders and keep track of their progress on the folders. Whether the students keep folders in their desks, cubbies, or are collected each day, there should be some signs of wear and tear.

(2). Rocket Charts on student folders show dates of each attempt to pass a level. Each day when students take a 1-minute timing test to try to pass a set of facts, they should write the date of the “try” on the Rocket Chart on the front of their folder. Without this record you cannot tell if a student is stuck because he or she has missed two weeks of school, or if students are only doing Rocket Math® twice a week (not recommended!), or if a student has exceeded six tries without intervention.

(3). Rocket Charts on student folders are colored in when passed. Coloring in the row on the Rocket Chart for the fact set that was just passed is the primary reinforcer of all that hard work. It is essential that students are given the time (and the colored pens, pencils, or crayons) to celebrate their success. Don’t get fooled by the older students or the students who are “too cool” to color in the chart. Even if they only want to color in the row with their regular pencil, students need to be told that they have accomplished something important, and giving them the time to color in their chart is a critical component of the program. This is way more important than you might think. You can also praise students who have accomplished a lot or who have just passed a level. Hearing from an administrator or coach about progress in math facts sends a huge message regarding the importance of the task.

(4). Student folders include packets of answer keys on colored paper. In order to practice correctly, each student’s partner needs to have an answer key in front of them when practicing. Each student needs their own answer key packet (so they can practice with someone who doesn’t have that answer key or with a volunteer who has no answer key). All the answer sheets for their operation should be copied and stapled into a booklet so students don’t have to go hunting for answer keys. Having the answer keys copied onto a distinctive color is important for teachers to be able to monitor paired practice. When students are practicing, each pair should have one student with answers (in that distinctive color) and the partner without the answers (on white paper). Any variation of this means the students are not practicing correctly—and that should be easy for the teacher to spot. Additionally, if a teacher is ready to begin testing and sees a hot pink paper on a desk, the teacher knows someone has answers in front of him or her.

(5) Student folders have the next sheet ready before starting practice time. Some system needs to be put in place so that the limited amount of time available for students to practice is NOT taken up with all students trooping up to the crate to get the next practice sheet each day. The recommended system in the Teacher Directions is to refill student folders when they pass a level, after school, with a packet of six sheets. That way the only time teachers have to handle folders is when students pass and they check the “pass” for errors and refill with a new packet. Many other ways of refilling student folders are possible, but no matter the process, students should have a blank practice sheet or set of practice sheets in their folder—which you would see when you check folders.

(6). Students have clear goals indicated on goal sheet. After students complete the Writing Speed Test, they are to have goals set for their daily 1-minute timing. The goal sheet should be stapled to the inside left of the student folder, the goal line circled, and the 1-minute goal written at the bottom of the sheet. The goal may be crossed out and a higher goal written in if the student has consistently demonstrated the ability to write faster than the original goal. Sometimes, teachers also write the goal on the front on the Rocket Chart, but the student’s goal should be clearly indicated. If not, it may be arbitrary or inappropriate (the same for all students, for example).

(7). Individual graphs are filled in because 2-minute timings are happening. Every week or two, students should be taking the 2-minute timings. These timings are a progress monitoring measure. They could be used for RTI or for IEP goals, or for any other time when a curriculum-based measurement is useful. At least they can demonstrate to us (and to the students) whether they are making progress in learning math facts in a given operation. As students learn more and more facts in the operation to a level of fluency and automaticity, they will be able to write answers to more facts in the operation on the 2-minute timing. Each time they take a 2-minute test, they should count the number correct and graph that on the graph stapled on the inside right of their folder. Each test is graphed in the correct column for whichever week of the month the test was taken.

(8). Individual graphs show upward trends as students are learning facts. Once students are taking the 2-minute timings regularly, it should be easy to see a trend. It should be going up, even if somewhat unevenly. For example, scores might go down after the long December break, but they should recover after a couple of weeks. If these graphs do NOT show an upward trend, something is wrong. Practice may not be being done for long enough (less than 2 minutes a day), or frequently enough (only three times a week), or students may not be practicing correctly (not fixing hesitations and errors). If only one or two students have flat graphs, those students will need something more. The individual graphs will be your indication that there is something amiss. You will just have to figure out what could be wrong. This should lead you to do some observations during Rocket Math® practice in that classroom.

Look at the Rocket Math file crate

(1). There is a crate or set of files for each operation practiced in the room. Each operation fills a crate and requires a different set of files. In any classroom where not all students are working on the same operation, there will need to be more than one set of files. Sometimes, teachers who have only one or two students in an operation may use the files of a neighbor teacher, but that should be only a temporary fix. The rule is that there must be a crate for every operation being practiced in that class.

(2). Rocket Math® crate is filled and organized from A–Z, complete with tabs. As of the 2013 version of Rocket Math®, every operation goes up to the letter Z. So each crate should have hanging folders with tabs showing the letters A though Z. Tabs are important to save time finding sheets and filling folders. If the files are a mess, out of order, no labels, or some letters are empty, valuable practice time will be used up trying to find the right sheets. If everything is labeled, and there are sheets in each file, then efficiency is a possibility. The Rocket Math store has tabs for sale if you need them.

(3). Rocket Math® crate has 2-minute timings numbered 1–5. In order to make sure that teachers do the 2-minute timing and monitor progress readily, they need to have class sets of the 2-minute timings (1 through 5) available in the crate. This is easy for you to check. If they are not there, it is likely that the 2-minute timings won’t be done as regularly as they should be. It is important for those timings to be done so you can see if all the students are making good progress.

(4). Teacher has a hard copy of the directions available for reference. The best place to keep the directions is right in the crate, so they are handy at any time. We have found that most of the time, when teachers are not doing things as they should in their Rocket Math® implementations, they don’t have a copy of the directions. When teachers don’t have the directions handy, they will ask a colleague how to do things. Unfortunately, this is like a game of telephone and typically doesn’t end well. Being sure that every teacher has the directions available for easy reference goes a long way toward proper implementation. It also allows you to pick up the directions when you are in the room and point something out to the teacher or to reference an appropriate page number in the directions in your notes to the teacher.

You can print the Teacher Directions from the virtual filing cabinet, in the Forms and Information drawer, under Rocket Math Teacher Directions.  You can buy printed copies from RocketMath.com/shop.  There are additional things to look for on the form but they are optional and go with supplemental parts of the curriculum.

Seven steps to an exemplary Rocket Math Worksheet implementation

You know already what should be happening.

This article assumes you have read the Rocket Math Teacher Directions yourself, so you know how things should run.  You can also read the Administrator and Coach Handbook for more ideas on how things should be running.  These helpful manuals can be purchased at their link, or available for free in the virtual Rocket Math Worksheet filing cabinet–in the Forms and Information Drawer. You’ll also need to have done observations using our observation form and checklist.    You should already know what things need to change–this is about how to make that happen.

How to make change happen.

These are recommendations as to how to get an implementation of Rocket Math® running smoothly, correctly, and effectively—without unduly annoying your teachers. How can you get every teacher in your building to abide by all the critical features of Rocket Math®? If teachers feel criticized, they will begin to resent the program and you. On the other hand, teachers (especially good teachers) are highly self-critical and, if they understand what should be happening, will enthusiastically self-correct a lot of details without you having to point out their errors. So here are seven steps to getting more of the enthusiasm and less of the resentment.

1. Choose one procedure to change at a time.

There may be several things not being implemented the way you would like (or as is outlined in the Teacher Directions). The temptation is to assign everyone to read the Teacher Directions and then follow them. Ask them to read the directions, yes, but they will need help to actually improve. To begin, just pick one concrete procedure that you want everyone to be sure to do the right way. Pick the most important one—as best as you can. Start with the top four of the observation form (shown here).

2. Talk about it first.

Always talk about needed details or techniques in a staff meeting before “noticing” the problem in any particular teacher’s room. If you see a problem in one or more classrooms, don’t ask those teachers to change as your first response. Instead, talk about what should be happening, in a staff meeting, without saying anything about those who weren’t doing it right. Describe clearly what you want teachers to do. Consider writing it down and passing it out as you talk about it. You may even need to have teachers practice it in a role-play scenario in small groups. This can be done for just a few minutes.

3. Give the rationale.

Whenever you talk about a feature or a technique you want teachers to do, explain WHY it is important. Explain it in terms of student learning. (The rationale is in the Administrator & Coach manual and in the Teacher Directions also.) Teachers want their students to succeed, so if you explain why it is important for the kids, the teachers will see the reason for doing it the right way. Have some discussion with the staff to make sure everyone knows both what you want and why it is important to learning.

Note: If you have a staff that doesn’t readily discuss, give them the questions you would ask, break them into groups to come up with an answer for each question, and have the groups report out.

4. Give a “heads up” that you’ll be observing.

At the end of talking in the staff meeting about the change you want to see, let everyone know that you will be visiting classrooms during Rocket Math® to see how things are going. If the change that you are looking for requires preparation, give a week’s notice. If it is just a way of doing things that can be changed immediately, start observing in the next day or two.

5. Follow through with praise first.

After observations where you see people doing what you wanted to see, be sure to tell them personally how impressed you are with their ability to implement a new idea so quickly or so well or with such enthusiasm. At the next staff meeting, after the end of the first observations, praise the people who are doing things well. If more than ¾ of your staff is doing it correctly, you can move on to observing for something new. If less than ¾ of your staff is doing the one specific thing correctly, then revisit the change and let your staff know that you will be visiting again within the next few days. Be sure to follow through with your visits.

6. Follow through with individual help.

Once you are down to a small number of staff members who are NOT implementing the change you want to see, it is time to offer more help to each of them. Once you see for the second or third time that a teacher is not implementing what is expected, tell them what you saw instead, and ask what you can do to help.

Be genuine. More often than not, teachers do not implement correctly because they don’t exactly know how, but were afraid to ask. Ferreting out what the stumbling block is, finding out what’s getting in the way of a good implementation, is the best use of your time. Sometimes, just role-playing what to say or do is needed. Sometimes resources are missing or haven’t been requested. Sometimes a method of organizing better is the key. Often, another teacher will have the key as to how to implement something—so don’t hesitate to use peers to support one another.

You should know that Rocket Math® done correctly will work. If you can get a teacher to do this well, they will be reinforced by the results. Students will end up being more successful, and that is very rewarding to any teacher who really cares. Staying with a teacher until the details are right will end up being worth the time—for you, for the teacher, and, most importantly, for the students.

7. Celebrate 100% implementation.

Keep track of the new things you’ve asked to be changed. Keep track of how many teachers are implementing. Keep praising those who are coming on board. Finally, celebrate when everyone “gets it.” Find a memorable way to celebrate the victory. Some people even create a “bragging list” of all the new procedures that were implemented to mastery by all the teachers in the school.

Teaching Math Fact Fluency | 6 Signs Your Class Is Failing

High-stakes state tests do not directly test fluency on math facts, although they should.  Your students can become bogged down in deriving basic facts during state testing.  When that happens they will be unable to demonstrate the higher-level math skills they have been learning.  You may have a math fact fluency problem, depressing your math achievement scores, but not even know it.  Here are six things to look for–to evaluate for yourself.

1) Finger counting during math testing shows a fact fluency problem

Students who are counting on their fingers (see above) during math testing are a definitive sign of a math fact fluency problem.  Finger counting is a bad sign in grades 3 and above, where they should have mastered math facts.  Students who don’t know the facts, need to use crutches to derive the answers to math facts.  Crutches make doing simple calculations take a long time to complete anything.  Your students may perform poorly on state tests just because they won’t complete the test for lack of time.

2) Students who lack math fact fluency need times tables available

When students in grades 3 or 4 and up have to do multiplication, they either have to know their facts or have a crutch.  If you see times tables on student desks that shows that the students need these crutches, and therefore do not know the basic multiplication facts.  Student folders sometimes come with these on the inside.  Some teachers put up a large poster of the multiplication facts–even though students find it nearly impossible to use from their seats.  Others provide laminated cards to the students which appear suddenly when students are set to do their “math work.”  When you see those times tables being used by more than a couple of students during math, you can tell you have a fluency problem.

3) Students who lack math fact fluency don’t participate in math lessons

Good teachers work to engage the class.  One good way, while working a problem for the class, is to ask the class for the answers to math facts.  Watching a lesson you may be able to spot a class that lacks fact fluency.  For example, imagine you watch the teacher demonstrating this problem.

Class, we begin this problem by multiplying nine times four.  What’s nine times four, everybody?”  [Only a couple of students answer.]  Yes, 36.  Now we write down the six and carry the 3 tens up to the tens place.  Next, we multiply nine times six.  What’s nine times six, everybody?”  [After a long silence, one student answers.] Yes, 54.  And we add the three to the 54, what do we get?  [Several students call out the answer.] Yes, 57.  That’s what we write down.

That interchange tells you there’s a math facts problem in this class.  When the problem is very easy, like 54+3 you get a good response.  When the fact is a “hard” one, you get silence and then one student answering.  Medium facts get minimal response.  This is a class that does not know their math facts.

4) Over-reliance on calculators signals a lack of math fact fluency

There are two kinds of over-reliance on calculators you may see in classrooms.  In the first kind, you see students who do not know facts using calculators to tell them the answer to single-digit facts they should have memorized.  Using calculators for single-digit facts is terribly slow and inefficient–and not what they are designed to do.  You can see this over-reliance on calculators when observing in a classroom.

The second kind of problem is harder to spot. Using calculators without knowing math facts instantly can be dangerous.  It is easy to make a data entry error, AKA a typo.  When a user does that, they’re assumed to know math facts well enough to know when the answer is wrong, as in the example pictured here.  A student who doesn’t know that 5 times 8 is 40 and therefore knows that 521 times 8 has to be more than 4,000 will accept the answer displayed on the calculator.  Accepting incorrect answers from the calculator is a sign that students do not have an adequate mastery of facts.

5) Avoidance behaviors in math signal a lack of math fact fluency

Having to count out facts or look each fact up in a table is very slow and onerous.  Students come to hate slogging through math computation that is so hard for them.  Conversely, students who know facts instantly, hop right into assignments to get them done.  Students like going fast doing math problems, just like they run for the joy of it on the playground.  How do you know there is a fluency problem in the classroom?  Students who lack fluency start avoiding getting started on computation work by getting water or sharpening pencils or just taking a break first.

6) Really slow computation during math lessons is due to a lack of math fact fluency

Good math teachers assign, within their lessons, a few math computation problems to do independently and then be checked as a group.  If students know math facts they can do a few problems in a minute or two.  Students who do not know math facts may take ten minutes or more to do the same mini-assignment.  Students who are done and waiting with nothing to do, begin talking and distracting the others.  When there’s that big of a discrepancy between the first and the last student to do a few problems, there is a fact fluency problem in the class.

To be sure–give school-wide 1-minute tests of math fact fluency

If you see hints that your school may have a math fact fluency problem, it isn’t hard to know for sure.  It only takes a couple of minutes.  You can have everyone in the school take written 1-minute tests of math facts pretty easily.  However, you’ll also need to evaluate how fast students can write.  Students can’t answer math fact problems any faster than they write.  You cannot expect a student who can write only 25 answers in a minute to answer 40 problems in a minute. Conversely, a student who can write 40 answers in a minute is not fluent with math facts if he answers only 30 problems in a minute.

You need a test of writing speed as well as a chart to evaluate their performance and the tests for the four main operations of addition, subtraction, multiplication, and division.  Print these out for free at this link.  But basically, a student who cannot answer math facts at 75% of the rate at which they can write, needs intervention.  

Learn more about teaching math fact fluency

Teaching math fact fluency is necessary, of course, for fluent computation. Math fact fluency is also required for understanding and manipulating fractions. Find out more ways of successfully teaching math fact fluency to your students and why this skill is essential.

If you would like the free use of use the Rocket Math Online Game to assess for fluency, please contact Dr. Don at don@rocketmath.com.

 

 

How to Set Math Fact Fluency IEP Goals (The Easy Way!)

Setting IEP goals and short-term objectives is a snap when you measure growth in fluency. Not only are fluency growth goals easy to write and set, but they are also easy to measure and monitor. You can adjust the intensity of the intervention ensuring the student can achieve the goals and objectives. Finally, you’ll be able to demonstrate growth and improve student achievement.

Child working on his math fact fluency iep goals

What are Math fact fluency IEP goals?

Math fact fluency goals are specifically designed to help students master basic math facts so that they can move on to more advanced topics. These goals should be tailored to each individual student’s level of understanding. They should focus on mastering basic operations such as addition/subtraction or multiplication/division, as well as developing problem-solving skills. In addition, these goals should also focus on increasing the speed at which the student can answer questions correctly in order to improve their overall math performance. 

Why are math fact fluency IEP goals important?

In addition to targeting academic performance, math fact fluency goals can also help improve overall mathematical fluency, which is defined as being able to solve mathematical problems quickly and accurately without relying too heavily on counting strategies or written algorithms. Mathematical fluency is important because it allows students to think critically about numbers and apply strategies learned from one problem type (i.e., fractions) across different contexts (i.e., decimals). Thus, having an IEP goal related to increasing math fact fluency can help foster overall mathematical fluency by providing students with the necessary building blocks for success in more advanced topics.

How to set math fact fluency IEP goals

When setting math fact fluency IEP goals, it is imperative to consider the student’s current abilities when determining the target goal. Each student should have individualized goals based on their specific needs and abilities. A good starting point for setting these goals would be to identify the number of correct responses per minute (RPM) that the student currently achieves and then set incremental increases from there. For example, if a student achieves five correct responses per minute (RPM), this could be the baseline starting point for setting future IEP goals. 

In addition to increasing RPM, other possible goals include mastering certain operations or combinations of operations within a given timeframe or reducing errors in computation tasks. The ultimate goal should be for every student to reach mastery over all four operations by the end of their educational program—which would equate to correctly answering all four operations at 10 RPM without any errors. 

Test the student’s present level of performance (PLOP) on math fact fluency

evaluation chart for pre-testIt only takes a minute or two to have students take a timed test in an operation to see how well they know their facts. You want to know how many facts the student can answer in that operation in one minute. Test first-grade students in addition and second-graders on subtraction. Starting in 3rd grade and up, multiplication has priority, so test and focus on multiplication facts for your IEP. You can move on to other operations once multiplication facts are fluent. Here is a link to a page with Rocket Math’s one-minute pre-tests in all four basic operations. However, you can’t evaluate whether a given student is fluent until you know how fast they can write. Students who are fluent with facts can answer them about as fast as they can write. But they cannot answer them any faster than they can write.

Test the student’s writing speed

writing speed test for match fact fluency iep goalsYou cannot set achievable goals of how many facts a student should answer in a minute without first knowing how fast they can write. That sets the upper limit. So test their writing speed by having them write a mix of one and two-digit numbers for one minute.  See above, the Rocket Math’s one-minute Writing Speed Test. From the link you can print it out for free. Once you know how fast your student can write you can evaluate their performance on the one-minute fluency tests.

Set the progress monitoring measure

If you’re going to test every week with 1-minute timings and you have a bunch of those available, you already have a 1-minute timing starting point.  If you’re using the Rocket Math Worksheet Program as your intervention, it uses 2-minute timings to measure progress weekly, so you’ll want to use one of those for your starting point. (You can’t double the 1-minute score because students don’t usually keep up at the same rate for two minutes.) So give one of the 2-minute timings in the operation you will focus on to set a starting point.

Set the math fact fluency goal based on writing speed

Students who have successfully developed math fact fluency in an operation can write answers to math facts almost as fast as they can write. As fast as their fingers can carry them is the most you could expect. You could set a goal at 80% of their writing speed. It would still be rigorous enough. If they met that goal the student would be fluent in math facts.

goal worksheet

You can do the math yourself from their writing speed test. The Rocket Math Worksheet Program has weekly progress monitoring 2-minute timings. In that case, your student’s goal for the 2-minute timing is on the handy goal sheet ** that you put into each student’s folder. You can see the student shown here filled in 36 boxes on the Writing Speed Test, so his or her goal for 2-minute timings would be 72 for the annual goal for the IEP.

Create a graph with an aimline

Now the coolest thing about progress-monitoring a fluency goal is that it is easy to graphically see on a weekly basis if the student is on track to meet the goal. You simply create a graph, with enough spots at the bottom for all the weeks in the year. Next you put in the starting point performance in the first week of the graph (or whenever you tested). Then put in your goal performance at the end of the year. Then draw a line between those two points. That line is called the aimline and is shown in the example below.

iep goals graph with an aimline

The student, whose aimline is pictured above, began at 29 problems in 2-minutes. Their present level of performance, or PLOP, was 29 problems correct in 2 minutes.  The student had a writing speed of 40 problems in a minute. Therefore 80% of that is 32 problems in a minute or an Annual Goal of answering 64 problems in two minutes by the end of the year. The aimline is simply a straight line between those two. You can see that the first couple of two-minute tests did not meet the aimline, but by the third test the student was right on track for meeting the goal by the end of the year.

Document the short term objectives (STOs)

short term objectives worksheetOnce the aimline is drawn, the STOs are found by reading up from the date of the quarterly STO reporting date. Wherever the aimline is on that date, that’s the STO. In the example above the quarter 1 objective looks to be about 38 problems in two minutes. The second quarter looks to be 45 problems in two minutes with the 3rd quarter at 53. Very simple and easy to set and to read and report. Since every student in Rocket Math should have a graph like this, reporting to parents on a quarterly basis would be no more than showing them this graph.

What if the student fails to meet the IEP goals?

child practicing math fact fluency iep goalsSo if a student is not meeting the aimline when we monitor their progress we should re-double our efforts. With Rocket Math that’s quite doable. If the student is falling below the aimline for three weeks in a row, add another practice session each day. The standard ten minutes a day for Rocket Math may not be enough for this student. So you need to arrange for them to get in another practice session each day. Often a daily short trip to the Special Education room for a second quick practice session with the teacher or an aide will do the trick. If two a day at school aren’t enough, maybe you can add one each evening at home. Some students do need more practice to meet these goals. The good news is that you can find out quickly with your graph and get going soon.

**The Rocket Math Goal Sheet was updated in 2021 to reflect the 80% expectation for IEP goals. The update shows that students who can fill in 15 boxes in a minute can go ahead and do Rocket Math, while those who can only fill in 14 boxes are candidates for help with writing numerals in the Rocket Writing for Numerals Learning Track.

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

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

Math fact fluency means instant recall

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

Math fact fluency makes math easy

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

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

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

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

How to assess students in math

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

 

Writing Speed Test

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

Get the One-Minute Rocket Math Writing Speed Test.

 

Operation Pretests

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

 

Evaluate Results 

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

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

Free Online Game subscription as long as you need to decide

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

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

 

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

The Online Game never teaches anything wrong.

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

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

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

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

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

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

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

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

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

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

Best Math Facts App Comparison: Rocket Math vs. XtraMath

A math facts app is a great tool to use for your students. There are plenty of math 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:

  1. 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.
  2. 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.
  3. 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.
  4. Both math facts apps only allow students to work for a few minutes (15 minutes or less) 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.
  5. 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 stand out.

An effective math facts app gives a student a sense of accomplishment

The difficult thing about learning math facts is persevering. 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

Screen shot of Mission Accomplished in the Rocket Math math facts app

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.

The Take-Off phase has only 4 problems to learn. They are repeated until the student gets 12 correct in a row. When the student does that, the doors close (with appropriate sound effects) to show “Mission Accomplished.” They also are congratulated by one of a cast of voices. Something along the lines of, “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!”

Congratulation screen shot from Rocket Math's math facts app

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. Rocket Math also has available Learning Track certificates from Dr. Don and the teacher for completing through Level Z.

An effective math facts app corrects errors—correctly

Neither of these math fact apps allows 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

comparison of two screen shots from Rocket Math’s math facts app

Rocket Math, however, requires the student to remember the answer. When a student answers incorrectly, the screen turns orange, and Mission Control displays and recites the correct problem and answer. In the pictured situation, Mission Control says, “Seven times nine is sixty-three. Go again.” Then the answer clears, and the game waits for the student to enter the correct answer. Under these conditions, the student has to listen to the correction and remember the answer, so they can enter it correctly.

Once the student correctly answers that target problem, the app presents the problem again. Then it presents it twice more interspersed with other problems.

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 facts 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

Time's up screenshot of the Rocket Math math facts app

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.

Keep Trying screen shot of Rocket Math math facts app

The app tracks errors, and three errors mean the student needs more practice on this part. The doors close (with appropriate sound effects). The student is given encouragement that they have defeated three hard problems and a challenge to “Keep Trying” if they are tough enough. At that point, the “go” screen appears, and the student has to hit “go” to open the doors (with appropriate sound effects) and 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, one of the cast of voices gives enthusiastic congratulations, as noted above.

Typically, students don’t have to “Keep Trying” 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 has a free version. It is $2 per student to have a few more options and $500 per school. 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, with part-time help from two friends. 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 $3 a year per seat (when ordering 100 or more seats). Twenty to 99 seats are $4 each. And fewer than 20 seats cost $5 each per year. As one principal customer of Rocket Math said, “We used to have XtraMath. We’d rather pay a little bit more for Rocket Math because the kids like it a lot better.” Another teacher reported, “My students are loving this program. I was using Xtra math, but now they are in love with Rocket Math!”

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

Document improved fluency by assigning a 1-minute RACE.

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

To Assign a Fluency Test 1-Minute RACE:

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

2) Click on the orange Bulk Action button.

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

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

Here’s what the students experience.

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

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

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

 

  • Export the test RACE results in spreadsheets. 

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

  • See averages across your class or school. 

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

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