How best to do peer teaching?

Why use peer teaching?

Compared to one teacher talking and a classful of students listening, peer teaching can greatly increase student engagement, and can massively increase time-on-task. Listening to a room full of students working together, practicing, and learning in pairs can be a thing of joy. If it is done right, there is nothing more effective for student learning. Research has shown that not only the student rehearsing but also his partner, the student checking the facts, learns from the process. Because all students can be fully engaged, a lot of practice can be accomplished in a short amount of time. However, sessions have to be structured carefully, and the task has to be something that lends itself to peer teaching.

What tasks lend themselves to peer teaching?

Peer teaching can’t work if neither student knows the material to be learned. You’ll have paired activities, but it won’t enhance or develop learning. Tasks that involve practice and review of previously taught material do lend themselves to peer teaching. Even better are tasks in which one student can have the answer key. You can be sure the correct answers are being learned with an answer key. Being corrected when you make an error is a key to learning, and that is not likely to happen without an answer key. The Rocket Math Worksheet Program is a good example of peer teaching. It involves paired practice of math facts, where one student practices and the other checks on an answer key.

How do you set up peer partners?

If you want to accomplish learning rather than facilitate socializing, you must set up peer partners. There is a saying, “Water seeks its own level.” This is definitely true of student pairs. Left to their own devices, the hard-working, conscientious students will pair up; unfortunately, the goof-offs will also pair up. And they won’t get anything accomplished. If you have an activity where it doesn’t matter what they accomplish, then it’s fine to let students pick their partners. But when you want them to be on-task and learning from the activity, you must set the partners.

Order your class list by focus and responsibility from top to bottom, then divide the list in half. Match the second half with the first half so that top students go with middle students and middle students go with bottom students. (See the picture to the right to get the idea.)

You want to have a responsible, on-task type student in each pair. You can avoid bitter enemies or students who have had problems in the past. But you do not need to match students up with their friends. They are here to practice, not to socialize. Also, do not give in to students who complain about their partners. Tell them “This is going to give you a chance to practice your ‘niceness skills’ which are important to learn. Even if you don’t like them, just do your work and practice your ‘niceness skills.'”

If you do have a volatile situation, you can change the partners, but be sure to change several pairs to obscure the real reason for the change. If students realize they can get out of having a partner by creating a bunch of drama, you’re in for a long year.

How do you avoid a lot of time lost in transition?

Once you’ve set up the partners, you have to set up a routine for “getting with your partner.” You can have a bunch of different solutions for getting with your partner. Some students may just turn around, while others bring a chair, and still others meet at a different part of the classroom. You need to explain to each student in each pair how they will “get with your partner.” 

Then once you have established that, you need to practice several times in row, “getting with your partner.” You want them to move smoothly and quickly, arriving with the correct materials and getting ready to begin immediately. Students must practice this several times, and perhaps a couple of days in a row. You want to stress that this should happen quickly and quietly. This is not a time to catch up with your friends or visit a new part of the classroom. Prompt the students with something like this, “Getting with your partner should happen how, everybody?” Students should answer with, “Quickly and quietly.” Then consider timing the transition to go for a record. You will be amazed at how quickly this can happen if everyone is focused, and a routine has been established. When you have quick and quiet transitions in your room, that’s the mark of a real pro!

How can you ensure effective practice and corrections?

You are going to have to teach an explicit set of procedures to students, so they know how to engage with each other. You will need to explain how to practice as well as how to correct errors. Then after teaching the correction procedure, you will need to make ALL of your students model the correction procedure. You do this by role-playing yourself as a student and calling on students to be your tutor/checker while everyone listens. Then you role-play making errors, so your tutor/checker can model the correction procedure. This lets you know if students are ready to work in pairs because they have demonstrated the correct procedures working with you.  Rocket Math its own script which you can use for how to get your students to model corrections. 

How do you keep the students on-task?

You must make the activity into an “endless task” that can continue until you say stop. That way, everyone must keep working, and there’s no excuse to stop. If there is an acceptable reason to stop working, e.g., “We’re done,” then students will stop working. When students can finish a task, they will. What’s more, they will say they are finished (because you can’t tell) even when they are not. Some pairs may never begin. You want a situation where everyone has to be working all the time, so you can have the same expectation for everyone the whole time. This is the reason students practice facts in Rocket Math in a circle, so they just keep practicing around and around until the teacher says stop. That’s an “endless” task, which is key to keeping students on task.  

You have to actively monitor the whole-time peers are practicing with each other.

Unfortunately, this is not a good time to get the attendance roster turned in. Or catch up on grading. You must treat this as an important activity if you want the students to do the same. You need to circulate among the students the whole time. You’ll need to bend down to get your ear next to their practicing so you can hear what is actually going on. You’ll be looking for student pairs that are following the approved (and modeled) correction procedure. When you hear that, stand up and publicly praise that pair so everyone can hear. “Wow, I just heard Tom and Betty doing a perfect correction procedure. They are really going to learn this material well. They are putting forth a real college effort.” Of course, if students are not on-task, be sure to remind them, and circle back to that pair soon, so they can redeem themselves by getting back on task.

How do you handle student disputes and controversy?

When a pair of students come up with a complaint, you can’t adjudicate it because you weren’t there! Therefore, repeat this mantra, “The checker is always right.” Then every time there is a dispute, repeat your mantra, “The checker is always right.” That means the checker’s ruling decides the issue, and you won’t overrule the checker, no matter how eloquent the complaint. If you keep saying the same thing all the time, like a broken record, students will come to realize you’re just going to say, “The checker is always right.” They will soon stop complaining altogether. Which will be a thing of beauty when it happens.

Peer teaching is only effective if managed well.

As you can see from the foregoing, there are several key management strategies that you need to employ to make peer teaching effective. 

  • You need to have the right kind of task assigned and to provide answer keys. 
  • You must set up the peer partners so that you have at least one conscientious worker in each pair. 
  • You need to establish a routine and speedy transition for students to “get with their partner” for peer teaching to begin. 
  • You need to teach students how to correct errors and ensure they’ve learned the procedure by making them model it.  
  • You must set up the task to be “endless” so that no students can get off-task because they are “done.”
  • You must actively monitor student engagement the whole time they are working. Actively monitoring means walking around, listening to them work, and loudly praising those who are doing it right. 
  • And finally, you have to teach them the mantra, “The checker is always right,” to settle disagreements and controversies. 

If you do this right, it will become your favorite time of the day. I know because it always was for me. 

To learn more teaching strategies to incorporate into your class, read my Teaching Strategie blog posts. From benchmarks to worksheets for kindergarteners, Rocket Math has all the tools to help push your students to success!

 

 

 

 

Math Fact Benchmarks: Guarantee To Meet Them With Student Effort & Rocket Math Online Game

Not meeting benchmarks: what should it mean?

When it comes to learning math facts, most students have had no opportunity to learn them in a systematic way.  Unless they have had an extraordinary school or an unusual teacher they have not received structured, systematic learning opportunities to memorize math facts. After three decades working in schools across the country, I know this to be the case.  Without systematic practice and effort, students will not meet math fact benchmarks. They won’t meet the Common Core expectation that students will “know [math facts] by memory.”   Whose fault is that?  It is not the student’s fault, nor the parent’s fault.  So “not meeting benchmark” should mean that here is an area where the school needs to provide some intervention to build fluency.

Are you certain your fluency intervention is effective?

The teacher and the school have an obligation to provide an intervention that is effective.  Some so-called “interventions” do not reliably produce increased fluency.  An essential part of using an intervention is to measure its effectiveness.  [That’s why IEP goals are supposed to have measurable short-term objectives!]  The best way to measure the effectiveness of a fluency intervention is with timed, curriculum-based fluency assessments.

If you measure the same way for the same amount of time, you can see if fluency is increasing. You can see that the student’s fluency is increasing if the student can complete more items during the timed test each time you measure. If the vast majority of all of the students improve in fluency, then you can be certain that the intervention is effective. The graph above shows that for Multiplication, 23,540 students have increased in fluency as they worked through the Rocket Math Online Game.  See evidence from all 16 Learning Tracks here.

Rocket Math Online Game is effective

As students work through the levels in each Learning Track in the Rocket Math Online Game, they are tested after completing the first level (A), then after completing 33% at level I, and then after completing 66% at level R, and then after they finish at level Z.  Each test is a 1-minute fluency test of a random selection of facts taught in that Learning Track.  Therefore, the scores are comparable. When the number goes up at each point in the curriculum, you can be sure that students are increasing in fluency.  The chart to the right shows site-wide data. You can see students improve on average as they work through the Learning Tracks in the Online Game.  You would not expect students to meet benchmarks until they have completed Set Z in the Learning Track.

Math fact fluency benchmarks in the Online Game: 16/minute in addition and subtraction.

The 1-minute RACEs in the Rocket Math Online Game are a good way to measure math fact fluency.  On average students exceed 16 per minute correct at Set Z and the average at the beginning is much less.  So a reasonable benchmark is 16 correct problems per minute.

The teacher can assign a 1-minute RACE at any time and the student will need to do it upon their next login.  The results will be available in the Review Progress screen as well as be exported from the button that gives “Results from Assigned races.”  However, the best measure of whether a student can meet the benchmark is after Set Z, when they have completed the Learning Track.  You can see the score by clicking on the pink button for exporting “Results from Scheduled Races.”

You can see the screenshot of an example of the results from scheduled races for all 16 Learning Tracks across our website.  You can see the Account Average shows improvement at each level.   Those scores after Set Z show that nearly all students are proficient by the end of the Learning Track.  So we know that the Online Game is an effective intervention.  But there’s a catch. At the Level Z test data there are no scores for students who had not completed Set Z in Multiplication.  Students have to actually play the game in order to learn.

Students must participate to learn: monitor and recognize effort

Assigning an effective intervention will not help unless students are engaged and participate.  Instead of reporting on benchmarks of academic achievement, why not report on benchmarks of effort?  Each time students login and complete a session (five, ten or fifteen minutes in length) on the Online Game their session is recorded towards their effort score for the last 14 days.  Students should complete a session every day in school and some at home for homework.  In the effort rating system every four sessions completed earns a star, so 15  completed sessions over the last 14 days earned the student to the left 3 and 1/2 stars.

If you monitor the effort scores and recognize students who are putting forth great effort, you’ll get more students participating.  Completing 12 sessions in the last two weeks is good effort and earns 3 stars.  16 sessions over the last two weeks would earn 4 stars!

You might consider giving out Star Effort Awards (available in the teacher section of the site) once a month for students who are putting forth super-star effort.  If you reward effort, we guarantee you’ll get achievement.   Soon after doing that, you’ll probably have to start awarding Learning Track certificates for students who are completing Learning Tracks. All awards are available on the admin page on Tab (K) in the main rainbow navigation bar.

 

 

 

 

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.

How to avoid unhealthy competition: Using the Wall Chart.

Competition may develop to unhealthy levels

When students begin to pass levels in Rocket Math, and color in the Rocket Chart in their folders, they naturally are proud of their accomplishments. Students want to tell me what level they are “on” when I visit classrooms.   Unhealthy competition may develop among students sometimes.  Some students begin to feel really bad about their slower progress, and students in the lead act arrogantly or disrespectfully.  The Rocket Math Wall Chart is designed to curb that competition.

The Wall Chart puts all the students on the same team.

star_sticker

Over 700 star stickers come with the Wall Chart.  Each time a student passes a level the teacher awards them with a star sticker, which they take up to the Wall Chart and put into one of the squares in the chart.  Students fill the chart from the bottom up.  The teacher sets a goal in a few weeks, which date is marked on the goal arrow, and the goal arrow is placed a couple of rows up from where the students are now.  (You can just see that in the picture above.)

 

Students develop pride in their whole class.

If the students fill in the squares up to the arrow–before the date specified on the arrow–they earn a group reward such as extra recess time, or music during math, or a congratulatory note home, or a popcorn party, etc.  Wall chart half filledIn this way, each time a student passes a level they are putting up a score for the whole team.  It is good for everyone.  The teacher is able to praise the class for their hard work and accomplishments, and the whole class is able to feel good about their collective effort.

The Wall Chart shows visitors (like principals) how well the class is doing.

Passers-by as well as interested administrators can praise the class as a whole for their successes with Rocket Math.  In many schools, classes post their completed Rocket Chart on their door with all 725 stickers in place!   The Rocket Math Wall Chart becomes a focus of pride and recognition for the whole class.  The price for the Rocket Math Wall Chart (#2005) of $20 includes directions, plenty of star stickers, four goal arrows, and the chart itself.   They are cheaper by the dozen, $155 for all twelve.

In What Order Should Students Learn Math Facts?

Learn the Basics (add, subtract, multiply, divide) first.

 

Basic, optional, and alternative—there are a lot of different Rocket Math programs to help students learn math facts. A common question teachers ask is in what sequence should they teach the various Rocket Math programs? The basic programs of Addition, Subtraction, Multiplication, and Division (1s-9s) have priority and must be mastered by all students. Addition in the first grade. Addition and Subtraction in the second grade. Multiplication (as well as Addition and Subtraction) by the third grade. Then, all four, including Division by fourth grade. If a student is on track, those basics have first priority.

 

Optional programs if the basics are already on track

 

The rest of the programs are optional and should be offered to students once the basics have been mastered and only then. The only exception would be in a school where Kindergarteners did not get a chance to learn how to quickly and easily write numerals, through using the Rocket Writing for Numerals program. 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).

Here’s a link to a printable version of the graphic above.

 

First-grade Students Should Learn Addition Facts

 

Students practicing their math facts together.If first-grade students are taking all year to get through sets A-Z in Addition, 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 with a better partner, and some may need to practice a second time during the day or at home in the evening. 

Another intervention would be to use Rocket Math Online Game for Addition facts, as students seem to progress much more quickly in the online game.  The Online Game has an adjustable game speed for first-grade students who are having trouble (their difficulty score is over 3) moving their fingers fast enough. First-grade students who finish the 1s-9s can move on to the Add to 20 programs for the remainder of the year.

 

Second-grade Students Must Know Both Addition & Subtraction Facts

 

The Rocket Math Online Game Additions fact family example page.

Second-grade students must have completed Addition before starting on Subtraction (1s-9s).  They can also test out of Addition through the Placement Probes which are available within the Addition drawer in the Rocket Math Worksheet program virtual filing cabinet. Addition has priority for second graders who can not test out of Addition in first grade or didn’t complete it in first grade. Only after getting through Set Z of Addition should they move into Subtraction. Second-grade students who complete Addition and Subtraction 1s-9s 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.

 

Fact Families is Another Way to Learn Addition & Subtraction Math Facts

 

 

A chart showing the Addition and Subtraction fact family of 2, 3, and 5.There is another way to learn facts, which is called Fact Families. 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.  

 

It is challenging for students to switch between Addition and  Subtraction. But it does drive home the reciprocal nature of the two. There is no evidence that it is better to learn in fact families than it is to separate the operations. That’s why we offer both alternatives. Students can learn fact families up to 10 in first grade. Then the upper fact families, from 11 in second grade.

 

Third-grade Students Must Learn Multiplication Facts

 

Third graders can begin the year working on addition and subtraction facts or reviewing them in fact families.  They should NOT begin memorizing multiplication facts until after they have learned the concept of multiplication in their math curriculum or use the Rocket Math Conceptual Multiplication learning Track.  After they have learned the concept of what multiplication is all about, then have them memorize Multiplication facts 0-9s.  Once multiplication is mastered, if there’s time, students who need to can go back to master addition and subtraction facts.

As in Addition and Subtraction, students can learn Multiplication and Division by fact families. In third grade, just the Multiplication-Division Fact Families through 20 need to be mastered. Once all three of these basic operations are under their belt I’d recommend the Identifying Fractions learning track next followed by the Factors learning track.

 

Fourth-grade Students Should Know Both Multiplication and Division Facts

Effective math teaching strategies help students of all levels be successful at math.

Fourth-grade students need to have completed Multiplication before going on to Division.  They can also do Fact Families for Multiplication and Division, starting with facts to 20 and then part two is fact families from 21 on. If they complete Multiplication and Division, they should go back and do Addition and Subtraction. If those are not mastered, either straight up by operation or in families. Then students can go on to Identifying Fractions, then Factors, then Equivalent Fractions. They can go on to 10s, 11s, 12s Division, but it is less valuable than the pre-algebra skills of factors and fractions.

 

Fifth-grade Students & Up Need to Know All Basic Operations First, Then Branch Out

 

Fifth-grade students should have completed all four basic operations (1s-9s). 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. Again, as an alternative, students can learn the basic facts in families. 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: Identifying Fractions, then Factors, followed by Equivalent Fractions, followed by Learning to Add Integers, Learning to Subtract Integers, then Mixed Integers.

 

Rocket Math Worksheet & Online Game

 

Learn more about Rocket Math: in just 2 minutes!  Rocket Math has a fun video for you to learn more about how Rocket Math works. Or check out our website at www.rocketmath.com 

Here is a quick and easy chart to help understand which operation/skill students need to learn in which grade level and which Rocket Math Worksheet and Rocket Math Online Game Level they should be at.

Age Grade Operation/Skill Rocket Math Worksheet Rocket Math Online Game Level
5-6 Kindergarten Writing Numerals Beginning Numerals

Rocket Writing for Numerals

In development
6-7 First Writing Numerals

Addition

Rocket Writing for Numerals

Addition 1s through 9s

Fact Families 1 to 10 Add and Subtract

Add to 20

Addition

Fact Families (+, -) to 10

Add to 20

7-8 Second Addition

Subtraction

Addition 1s through 9s

Fact Families 1 to 10 Add and Subtract

Add to 20

Subtraction 1s through 9s

Fact Families 11 to 18 Add & Subtract

Skip Counting

Subtract from 20

Addition

Subtraction

Fact Families (+, -) to 10

Fact Families (+,-) from 11

Add to 20

Subtract from 20 

8-9 Third Multiplication Multiplication 1s to 9s

Multiplication 10s, 11s, 12s

Identify Fractions

Multiplication

Fact Families (x,division) to 20

Multiplication 10s-11s-12s

Identify Fractions

9-10 Fourth Multiplication

Division

Multiplication 1s to 9s

Division 1s through 9s

Multiplication 10s, 11s, 12s

Division 10s, 11s, 12s

Identify Fractions

Equivalent Fractions

Factors

Multiplication

Division

Fact Families (x,division) to 20

Fact Families (x, division) from 21

Multiplication 10s-11s-12s

Division 10s-11s-12s

Identify Fractions

Equivalent Fractions

Factors & Primes

10+ Fifth and up All Basic Operations

Fractions

Positive/Negative Numbers

Basic Addition, Subtraction, Multiplication, and Division

Equivalent Fractions

Factors

Learning to Add Integers

Learning to Subtract Integers

Mixed Integers

Basic Addition, Subtraction, Multiplication and Division 

Identify Fractions,

Equivalent Fractions,

Factors & Primes,

Fraction & Decimal Equivalents (coming soon)

 

The Ultimate Guide to Math Fact Fluency

Students counting on their fingers is a sure-tell sign that they didn’t acquire math fact fluency. It is sad to see students, ashamed of the only thing they know, counting on their fingers under their desks. Our elementary educational mission is failing students who haven’t developed math fact fluency, which  is the foundation to more advanced math skills.

Developing math fact fluency takes structure, organization, and work on the part of both teachers and students. In this article, I will share everything you need to know about developing math fact fluency.

What is Math Fact Fluency

Math facts are single-digit problems such as 7+9 or 6×8 or 14-5, and so on. A common name for all the multiplication math facts is the “multiplication table.” Math fact fluency is the ability to answer all math fact questions instantly from recall without having to think through the problem.

Students should be able to recall math facts instantly without having to count on their fingers or  hesitate to think about the answer. This may seem like a high bar, but our brains are great at recalling an unbelievable amount of information daily, and with practice, math facts can be recalled the same way. 

Three Reasons Why Math Fact Fluency is Important

tools to build math fact fluencyMath fact fluency is critical because it is a “tool skill.” Meaning, it is a tool that is used in the process of doing other math problems. Developing this tool skill makes learning math easier as concepts get more complicated. This tool skill needs to be automatic in the student’s brain, in order to save precious short-term memory resources.

Math fact fluency can be compared to reading. Students must recognize words automatically to comprehend the author’s meaning. Otherwise, they will spend too much time decoding individual words.

 

 

When students are fluent in math facts, they are focused on the math process as a whole, rather than stopping to puzzle out the facts. This is important for three reasons: 

1. Students with math fact fluency make fewer errors

Students who lack math fact fluency often make careless errors doing arithmetic computations . If they devote too much energy to deriving math facts, they lose sight of the problem at hand and make mistakes that would otherwise be obvious. Those who can effortlessly recall math facts can concentrate on what they are doing, and ultimately make fewer errors.

2. Math fact fluency makes learning math easier

When a new math procedure is introduced, students who have math fact fluency can easily follow the thread of instruction. Without this fluency, students fall behind instruction or demonstrations as they try working out math facts. This distraction takes away from a student absorbing all of the details necessary to successfully learn new math processes.

The first teacher to use Rocket Math to teach subtraction facts to her second graders realized the benefit first hand. She told me that with Rocket Math, she was able to teach regrouping in subtraction in just three days.

Her students mastered the math facts, and the outcome was extraordinary. The teacher shared that since these students had developed fluency in subtraction facts, they were able to learn other procedures easily.

3. Students who have developed math fact fluency enjoy math and always complete their work

Having to count on your fingers or look up facts on a timetable is slow and onerous. When students can’t work quickly, math problems become a dreaded drudgery. Students are motivated by mastering new skills, which will help them work faster and build confidence . Those who can quickly recall math facts will complete their work with ease , and enjoy the feeling of accomplishment.

 

How to Build and Improve Math Fact Fluency

steep climb to math fact fluencyBuilding and improving math fact fluency requires a systematic effort over the elementary years. It is a long climb to achieve mastery and there are no short-cuts.

Consistent daily practice throughout elementary school is important for retention. Slow and steady wins the race when building math fact fluency.

Math fact practice should be structured in such a way that students are learning a small number of facts at a time. These small groups of facts  should be practiced daily until students have reached mastery. As time goes on, more groups of math facts are introduced systematically in small amounts for students to master.

Learning 1s to 9s facts in the four basic operations will take elementary students months to master. Worksheets and game applications are two of the best ways to teach math fact fluency over time. Combining structured math fact learning, practice, and evaluation with fun math fact games helps students develop number sense and understand complex numerical relationships.

 

Teaching Math Fact Fluency with Worksheets

Worksheets are popular tools that teachers reach for when teaching math facts, but sadly, they often fall short for the majority of students. A few select students will begin memorizing the facts on their own accord in order to make the worksheets easier, but most students will continue to slowly work out the facts either on their fingers or in their heads. These students may never develop a strong recall of the facts and become flustered when asked to answer problems on the spot.

Fortunately, there are specific worksheets that are effective in building math fact fluency. The key is having worksheets that are structured, systematic, and sequenced. Each worksheet should only have two to four facts to be learned. 

By working on only two to four facts, these worksheets help teach memorization for a strong recall, rather than reinforcing working out problems slowly. Students  will then be able to remember these small groups of facts easier, and by the end of the worksheet will be writing answers from memory. 

 

Teaching Math Fact Fluency with The Rocket Math Worksheet Program

Two students participating in one of Rocket Math's math fluency programsThe Rocket Math Worksheet Program improves upon this concept by using paired practice and saying facts aloud. Students partner up and practice quickly recalling facts together. One student asks the questions and watches for when their partner hesitates to answer. He or she then gives his or her partner more opportunities to practice the harder facts.

The students switch roles, and after both have answered questions, they then take a one minute test on the facts that they have learned so far. If students are answering as fast as their fingers will carry them, then they pass the level and move on to the next worksheet in the sequence.

Ten minutes of practice  every day gets the job done, especially when paired with using these facts in higher level math problems.

 

Teaching Math Fact Fluency with Games

Students and teacher playing multiplication games with dice sitting in a circle in a classroomIn addition to worksheets, schools of education tell teachers to use games to “teach” math facts. Unfortunately, most games and fun activities do not actually help individual students learning math facts to the level of fluency. These games, such as bingo or dice, have several fallouts:

  • Students spend most of their time waiting for their turn rather than practicing facts.
  • They do not focus on teaching a small group of facts in a manner that helps students commit them to memory.
  • The games do not adjust to an individual student’s level of fluency.
  • Students can pace the game slowly enough to have time to figure out facts rather than requiring recall.
  • It is difficult to keep every student engaged, as those who are behind are less likely to participate.

Using the Rocket Math Online Game as an Effective Way to Teach Math Fact Fluency

asian child holding tablet with a math fact fluency app by Rocket MathThere are games that are very effective at building math fact fluency. Games such as the Rocket Math Online Game have several important features that make a big difference.

  1. Every student is engaged in answering math facts—not waiting for a turn.
  2. Students learn only a few new facts at a time so that they can remember them.
  3. The game provides lots of focused practice on each set of facts. 
  4. The game requires students to answer quickly, which guarantees the students recall the answer rather than “figuring it out” over and over.
  5. The game gives an immediate correction and extra practice on any facts that students cannot answer quickly and correctly.
  6. The game only introduces new facts once students demonstrate mastery of facts learned so far.
  7. The game gives students explicit feedback so they have a sense of accomplishment as they work their way through an operation.

Math Fact Fluency Benchmarks

The following benchmarks are reasonable expectations for a school that has an effective math fluency program in place. Of course, a student cannot write math facts any faster than they can normally write, so take that into account when looking at fluency benchmarks. Adjust the benchmarks for students who do not write quickly. 

Kindergarten Numeral Writing Fluency Benchmarks (digits)

Start of Year Mid-Year End of Year
  20 digits per minute 40 digits per minute
 

First Grade Numeral Writing Fluency Benchmarks (digits)

Start of Year Mid-Year End of Year
40 digits per minute 60 digits per minute 60 digits per minute
 

First Grade Math Fact Fluency Benchmarks (problems per minute)

Start of Year Mid-Year End of Year
Addition: 12 per minute Addition: 25 per minute Addition: 25 per minute
 

Second Grade Math Fact Fluency (problems per minute)

Start of Year Mid-Year End of Year
Addition: 25 per minute                      Addition: 30 per minute                      Addition: 30 per minute
  Subtraction: 12 per minute Subtraction: 25 per minute
 
Third Grade Math Fact Fluency Benchmarks (problems per minute)
Start of Year Mid-Year End of Year
Addition: 30 per minute Addition: 30 per minute Addition: 30 per minute
Subtraction: 30 per minute Subtraction: 30 per minute Subtraction: 30 per minute
  Multiplication: 30 per minute Multiplication: 30 per minute
 
Fourth Grade Math Fact Fluency Benchmarks (problems per minute)
Start of Year Mid-Year End of Year
Addition: 35 per minute Addition: 35 per minute Addition: 35 per minute
Subtraction: 35 per minute Subtraction: 35 per minute Subtraction: 35 per minute
Multiplication: 35 per minute Multiplication: 35 per minute Multiplication: 35 per minute
  Division: 20 per minute Division: 35 per minute
 
Fifth Grade Math Fact Fluency Benchmarks (problems per minute)
Start of Year Mid-Year End of Year
Addition: 35 per minute Addition: 40 per minute Addition: 40 per minute
Subtraction: 35 per minute Subtraction: 40 per minute Subtraction: 40 per minute
Multiplication: 35 per minute Multiplication: 40 per minute Multiplication: 40 per minute
Division: 35 per minute Division: 40 per minute Division: 40 per minute

 Math Fact Fluency Assessment

Use this printable packet of free math fact fluency assessments to test your students’ skill levels relative to  the above benchmarks. This will give you a clear idea of your students’ fluency and where there is room for opportunity.

Rocket Math’s assessment packet includes a writing speed test, which helps create realistic expectations for individual students. Using the goal sheet ensures you will evaluate the individual student math fact fluency in light of their writing speed.

Rate students as:

  1. Weak, needs fact work
  2. Good, but fact work could help
  3. Strong, fact work not needed

Special triage priority: if you have fourth-grade students and above, start with multiplication facts. Multiplication facts are essential to future success in math above fourth grade. Even if fourth graders are counting on their fingers for addition and subtraction, teach multiplication mastery first. If fourth graders move to the next grade without strong multiplication fact fluency, they will have a hard time successfully progressing through math.

 

The Best Tools for Developing Math Fact Fluency

With the right tools, any student can develop math fact fluency and have fun while doing it! Students use Rocket Math’s Subscription Worksheet Program to practice with partners, then take timed tests. Rocket Math also offers math facts practice online through the Rocket Math Online Game. Students can log in and play from any device, anywhere, any time of day! Start a free trial today. 

Both the worksheet program and the online game help students master addition, subtraction, multiplication, and division math facts for a lifetime of success in math.

 

 

 

Positive Praise: Building Effective Teaching Habits

Positive praise is one of the most effective ways to encourage wanted behaviors from students. Because building habits is not an easy task, here are a few things you can do to start easily incorporating positive praise in the classroom.

  1. Be prepared with positive phrases
  2. Develop the most effective wording
  3. Start Small with two areas you would like to see improved behavior
  4. Practice in the Classroom and watch the effect it has on your students
  5. Grow and expand your positive phrases over time as you master the habit

Be Prepared with Positive Praise Phrases

I distinctly remember trying to help pre-service teachers build the teaching habit of positive praise. I would make suggestions and then observe. Trying to implement my suggestions wasn’t as easy as you would imagine – these teachers would glance in my direction and start the sentence “I like the way you’re . . .” and then trail off without knowing what to say.

Teachers want to use positivity and affirmation with their students, however, in my experience, they don’t always have the appropriate words ready to praise good behavior. Building the teaching habit of positive praise starts with getting the right words ready.

Recently I was reminded of this key component of building the new habit of making more positive statements. I wanted to personally develop this positive statement habit, but for some reason was not making the progress I had hoped for.

I quickly realized that I was making the same mistake I had watched the pre-service teachers make. I was unable to make more positive statements because I did not have any in mind that were ready-to-use.

To build the habit of making more positive statements, I would have to start memorizing some key phrases to keep on standby, ready to use when I needed them.

Positive Praise Example Phrases: How to Develop the Right Wording

The first step in positive praise is learning and developing the most effective wording. Using effective wording means you are getting through to your student, and clearly communicating that you appreciate the good behavior they are exhibiting.

Praise is most effective when it is prompt – when you deliver the praise in the moment. Can you picture a specific scenario in your classroom when many of the students are not doing as you asked, while a few students are dutifully following instructions?

This is the perfect scenario to use positive praise not only in rewarding students with good behavior but also encouraging other students to follow suit. Don’t be afraid to praise good behavior loud and proud for the rest of the classroom to hear!

Here are some examples of positive praise:

  • Look at Alan so smart sitting in his seat and showing me he is ready to learn. Way to go, Alan.
  • I see Beto is tracking with his finger while Claudio is saying the facts. That’s the way to help your partner!
  • Julia, you are so sharp having your eyes on the teacher, so you can learn!  I am impressed.
  • Stacy and Sophia know just what to do, they have their books open to page XX.  They are so on top of it!
  • Fantastic, Justin! You put your pencil down and are waiting for directions.  I can tell you’re going to college.
  • Stephanie is being such a great on-task student by working quietly and not talking.

Start Small: Pick Two Key Behaviors You Would Like to See More Of

Start out by choosing wanted behaviors from the two most annoying or frustrating scenarios you face as a teacher.  Stating small will help you build a consistent habit of giving positive praise.

Take these two wanted behaviors and build two praise statements you can easily use in-the-moment. Make sure the statement names the behavior specifically. Always include the student’s name, and keep it simple and affirmative.

Now, take a note card or piece of paper and write down these two statements. Don’t wait! Write them down now and keep this note in front of you while you teach. It will serve as a reminder throughout your day to incorporate positive praise as much as possible.

Practice saying these phrases aloud until you have them memorized and can recall them without having to think about it. The most important step in building this habit? Actually practicing positive statements in the classroom.

With these key components and diligent practice in the classroom, you will quickly build the habit of positively praising your students.

Positive Praise in The Classroom: Will it Make a Difference?

Fortunately, positive praise is free and can be implemented at any time throughout the school year. Start using positive praise now, and watch how your students respond.

Prepare yourself for giving positive praise when you are about to begin those frustrating scenarios. When the activity begins, look for opportunities to praise the behavior you are looking for when you notice students who are off-task.

You will see results when you use positive praise genuinely and with enthusiasm. You will know it is working if you watch for those distracted students taking notice of who is being praised. If you notice this happening, keep it up. The more praise you give for wanted behavior, the more that behavior will occur.

Grow and Expand Your Positive Praise Habit

Now that you know how to promote a specific behavior with positive praise, you can systematically develop statements for all your troublesome areas.  Every time students are not doing what you want, think of what you want them to do instead.  Behavior analysts call those replacement behaviors. 

Positive praise can also be used creatively alongside other motivational tools in the classroom. When I began my teaching career I was in the habit of scolding behaviors I did not want. Early in my career, I learned the effectiveness of positive praise and began incorporating it into my daily routine.

When I saw the behavior I wanted I would give loud and proud praise for all to hear. I decided to couple this by adding marbles to a jar every time I gave praise, as an added motivational tool – so students could see how well they have been doing. It worked wonders on increasing wanted behavior.

Building new habits is never easy, but I can personally say that as a teacher, learning to incorporate positive praise into your teaching routine will not only help students learn, but it will save you a lot of frustration!

If you are currently looking for a job as a math teacher abroad, check out this link on Jooble.

Rocket Math Adds Beginning Numerals & Counting Program

A screenshot of Rocket Math’s Beginning Numerals counting worksheet showing how students choose the numeral besides the images to show how many objects are in an image.

Beginning Numerals and Counting

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 and is to help them learn counting and numerals. That means they can’t learn on their own, the teacher must provide instruction. Teachers can use the counting objects kindergarten 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 above.

If you’re already a Rocket Math Universal Level subscriber, you can find the worksheet in your virtual filing cabinet. Not a subscriber yet? Get the counting worksheets.

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 three 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

A screenshot of the worksheet portion You Do, with a grid of three by five squares each with images to count and numbers to choose from.

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.

 

Rocket Math’s Counting objects worksheets for Kindergarten

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.

If you’re already a Rocket Math Universal Level subscriber, you can find the worksheet in your virtual filing cabinet [use your link]. Not a subscriber yet? Get the counting worksheets.

 

 

In What Order Should Students Learn Fast Math Facts?

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. Here’s a link to a printable version of the different Rocket Math programs shown here.

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.

A chart that shows the set of math fact family 5, 3, and 2 in Addition and Subtraction.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.

Optional Programs

The rest of the fast math facts programs like Rocket Writing for Numerals or Skip Counting are optional. You should only offer these programs to students once they have memorized the fast math facts through the Basic Program or the Alternative Program.

The only exception would be in a school where Kindergarten students did not get a chance to learn how to quickly and easily write numerals. In that case, you might take the first two months of the first grade year to run students through Rocket Writing for Numerals before beginning Addition (1s-9s).

Let’s take a closer look at how to implement each program in different grade levels.

First grade math facts: Learn Addition

Rocket Math fast math facts programs for first graders include:

  • The Basic Program
    • (1s-9s) Addition
  • The Alternative Program
    • Fact Families (1-10) Add & Subtract
  • Optional Programs
    • 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
    • (1s-9s) Addition
    • (1s-9s) Subtraction
  • The Alternative Program
    • Fact Families (1-10) Add & Subtract
    • Fact Families Part Two (11-18) Add & Subtract
  • Optional Programs
    • Subtract from 20
    • Skip Counting

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)
    • (1s-9s) Addition
    • (1s-9s) Subtraction
  • Optional Programs
    • 10s, 11s, 12s Multiplication
    • Factors

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)
  • Optional Programs
    • 10s, 11s, 12s Multiplication
    • Factors

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:

  1. Factors
  2. Equivalent Fractions
  3. Learning to Add Integers
  4. Learning to Subtract Integers or Mixed Integers

Does Your Kid’s App Teach Math Fact Fluency – Or Waste Time?

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:

  1. The app has to tell the problem and the answer to the student.

  2. It has to ask the student to give the correct answer to the problem.

  3. 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.