Beginning numerals and counting program added to Rocket Math

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.  That means they can’t learn on their own, the teacher must provide instruction.  Teachers can use the worksheets to effectively teach students to count objects aloud and then match the word with the numeral. You can see the top half of Worksheet A here.

I do–demonstration of counting.

Each worksheet begins with a demonstration of counting objects and circling the numeral that matches.  On Worksheet A there are only the numerals two and three to learn.  The teacher demonstrates (best with a document camera so all students can see) how she counts the objects and then points out that the answer is circled. Suggested teaching language is something like this,

“I can do these. Watch me count the frogs. One, two, three.  There are three frogs in this box. So they circled the three. Everybody, touch here where the three is circled. Good.
How many frogs were in this box, everybody? Yes, three.
Now watch me do the next box.”

We do–counting together. 

In the “We do” portion of the worksheet the teacher counts the stars first as a demo and then with the students.  Worksheet A you all just count 3 stars.  Suggested teaching language is something like this:

“Our ‘We Do’ says to touch and count. Start at zero and count each star.
We are going to touch and count the stars. Put your counting finger on zero,
everybody. We are going to start at zero and count each star. Let’s count.
One, two, three. We counted three stars. That was great!
Let’s do it again! Fingers on zero, everybody. Let’s count. One…”

By Worksheet S the teacher and the students are  counting 12 stars together.

The program has a page of teacher directions, with suggested language for teaching the worksheets.

You do–independent counting. 

In the “You do” portion of the worksheet (after learning the numerals with the teacher), the students are asked to count the items in each box and circle the correct number.  They are not asked to form the numerals–that’s numeral writing skill.  They just identify the numeral and circle it. Besides cute items there are also dice to count, fingers to count and hash marks to count–so students can learn multiple ways of keeping track of numbers.

Passing a level requires 100% accuracy.  Students who make any errors should be worked with until they can complete the worksheet independently and get all the items correct.

This Beginning numerals program will build strong beginning math skills for kindergarten students learning the meaning of numerals.  Combined with Rocket Writing for Numerals it will set students up for success in elementary math.

 

 

How School Math Fluency Programs Work

Math Fluency Programs should be part of on-going elementary school routines

Most elementary teachers do some activities to promote math fluency.  Yet many elementary children are not fluent with math facts by the time they hit upper elementary or middle school.  A hit-or-miss approach allows too many students, especially the most vulnerable, to slip through the cracks.   Math fluency programs, like Rocket Math’s Worksheet Program, need to be part of your elementary school’s routine.  Effective math fluency programs should be properly structured and every math teacher should be on board, every year.

Math fact fluency enables students to develop number sense

Many teachers learn in their training programs about the importance of “number sense.”  Students who have “number sense” can easily and flexibly understand relations between numbers.  They can recombine numbers in various ways and see the components of numbers.  Students with number sense can intuit the fact that addition and subtraction are different ways of looking at the same relations.

What is not taught in most schools of education is that developing fluency with the basic math facts ENABLES the development of number sense much better than anything else.  Once students memorize facts, they are available for students to call upon to understand alternate configurations of numbers. Students find it much easier to see the various combinations when they when they can easily recall math facts.  Once students master the basic facts, math games that give flexibility to thinking about numbers become much easier.

It may be hard for new teachers, straight from indoctrination in the schools of education, to imagine this is true.  However, if they land in an elementary school with a strong math fact fluency program they will see the beneficial effect of memorization.

young boy wearing a blue striped shirt counting to seven on his fingersWhy is math fact fluency important

In the primary grades, students who have not developed fluency in math facts will have a harder time learning basic computation.

Students who are not fluent with math facts find the worksheets in the primary grades to be laborious work.  They finish fewer of them and may begin to dislike math for this reason.

By the time students reach upper elementary, if they have not memorized the math facts, they find it very difficult to complete math assignments at their grade level.  They find themselves unable to estimate or do mental math for problem-solving.  The need to figure out math facts will continue to distract non-fluent students while they are learning new math procedures like algorithms.

In the upper grades, their inability to figure out multiplication facts becomes a huge stumbling block.  Manipulations of fractions, decimals, and percentages will not make intuitive sense to students because they haven’t memorized those facts.  Without math fact fluency, students rarely succeed in pre-algebra and may be prevented from learning algebra and college-level math entirely.

Math fact fluency must be assured through regular monitoring

Some students will need up to ten times more practice to develop math fluency than other students.  Therefore, monitoring student success in memorizing the facts is critical. Teachers can assume that what is “enough practice” for some students is NOT going to be enough practice for all students.  Effective math fluency programs must have a progress monitoring component built in.  Progress monitoring gives comparable timed tests of all the facts at intervals during the year.  Teachers look at the results of these timed tests to check on two things:

1. Are students gradually improving their fluency with all the facts gradually over the year? 

In other words, are students able to answer more facts in the same amount of time?  If they aren’t improving, then the instructional procedures aren’t working and need to be modified or replaced.  Math fluency programs like Rocket Math’s Worksheet Program have two minute timings of all the facts in each operation that can be given and the results graphed to see if there is steady improvement.

2. Are all students reaching expected levels of performance at each grade level each year?

Proper math fluency programs identify students who are not meeting expectations and give them more intensive interventions.  Ultimately, by the end of fourth grade all students should be able to fluently answer basic 1s – 9s fact problems from memory in the four operations of add, subtract, multiply and divide. Fluent performance is generally assumed to be 40 problems per minute, unless students cannot write that quickly.

Expectations vary by grade level and the sequence with which schools teach facts can vary.  While it is great to achieve all that the Common Core suggests, it is critical only to assure that students master and gain fluency in 1s through 9s facts.  Some schools in some neighborhoods may find that waiting until second grade to begin math facts may not provide enough time for all students to achieve fluency.  When to begin fact fluency and how much to expect each year should be based on experience rather than some outside dictates.

Successful math fluency programs must have these 3 features

 

  1. Sequences of small sets

    No one can memorize ten similar things, like the 2s facts, all at once. Students easily master math facts when they can learn and memorize small amounts of facts at one time. Effective math fluency programs define math fact sequences, which students memorize at their pace before moving onto new math facts. Rocket Math’s fluency program uses only two facts and their reverses in each set from A through Z.

  2. Self-paced progress

    Even if you only introduce small sets of math facts, some students need more time to memorize than others.  If you introduce the facts too fast, students will begin to jumble them together and progress will be lost. The pace of introducing facts must be based on mastery—not some pre-defined pace.  This is why doing all the multiplication facts as a class in the first six weeks of third grade does not work.  It is just too fast for some students.  Once they fall behind it all becomes a blur.

  3.  Effective practice and corrections

    When students are practicing facts, they will come to ones they have forgotten or can’t recall immediately.  Those are the facts on which they need more practice.  Allowing students to stop and figure out the facts they don’t know while practicing, does not help the student commit them to memory.  Instead, students need to IMMEDIATELY receive the fact and the answer, repeat it and try to remember it.  Then they need to attempt that fact again in a few seconds, after doing another couple of problems.  If they have remembered the fact and can recall it, then they are on their way to fluency.  But students must practice the next day to cement in that learning.

Math fluency programs like Rocket Math’s Worksheet Program teach students math facts in small sets, allow students to progress at their own pace, and support effective practice and error correction. Each Rocket Math Worksheet program has 26 (A to Z) worksheets specially designed to help kids gradually (and successfully) master math skills. Gain access to all of them with a Universal Subscription or just the four basics (add, subtract, multiply, divide–1s to 9s) with a Basic Subscription.

 

 

Why Multiplication Games Are Awful & What to Do About It

As a university supervisor of pre-service teachers, I’ve seen my share of bad lessons.  Among the most painful were when student teachers would try to liven up their lessons to impress me by having the students do a math game.  My student teachers wanted their students to learn math facts and to do so in a fun way.  The picture above is typical of what I would see.  Here are the reasons that most multiplication games that the student teachers implemented were awful.

(For multiplication games that work in and out of the classroom, check out Rocket Math’s Worksheet Program and Online Game.)

Waiting for your turn at a multiplication game is not learning!

As you can see in the picture above, all but one of the students are just waiting for their turn.  They aren’t doing math.  The students are just watching the student who is playing.  No one likes waiting, and your students are no exception.  Any game that has turn-taking among more than two students wastes time.

Make sure your multiplication games are structured so all or most students are engaged and playing all the time.  You want students to have as much engaging practice as possible while practicing math facts at speed.  If everyone can be doing that at the same time, that’s optimal.  No more than two students should be taking turns at a time.

A multiplication game that allows using a known strategy to figure out facts (like finger counting) is not learning!

Learning math facts involves memorizing these facts so that students know them by memory, by recall.  Committing facts to memory is why there is a need for lots of practice.  If the game allows time for students to count on their fingers or use some other strategy for figuring out the answer to facts, then there is no incentive for students to get better.

In the lower left corner of the picture you can see one student counting on their fingers—which is better than just watching—but is not learning the facts, it is just figuring them out.  The most able students in an elementary school are able to memorize facts on their own when they tire of figuring them out day in and day out.  But the rest of the students will just do their work patiently year after year without memorizing if you don’t create the conditions for them to memorize facts.

Make sure that your multiplication games reward remembering facts quickly rather than just figuring them out.  Speed should be the main factor after accuracy.  Fast-paced games are more fun and the point should be that the more facts you learn the better you’ll do.

Multiplication games that randomly present ALL the facts make learning impossible.

It is a basic fact of learning that no one can memorize a bunch of similar things all at once.  To memorize information, like math facts, the learner must work on a few, two to four facts, at a time.  With sufficient practice, every learner can memorize a small number of math facts. Once learners master a set of math facts, they can learn another batch.  But if a whole lot are presented all at once, it is impossible for the learner to memorize them.

Make sure your multiplication games are structured so that each student is presented with only facts they know.  A good game presents only a few facts at a time.  As students learn some of the math facts, more can be added, but at a pace that allows the learner to keep up.  The optimal learning conditions are for the learner to have a few things to learn in a sea of already mastered material.

Rocket Math Multiplication Games

We designed Rocket Math games to help kids gradually (and successfully) master math skills. Students use Rocket Math’s Worksheet Program to practice with partners, then take timings. Students can also individually develop math fact fluency—from any device, anywhere, any time of day—with Rocket Math’s Online Game.

Math Teaching Strategy #1: Help students memorize math facts

Once students know the procedure, they should stop counting and memorize!

When it comes to math facts like 9 plus 7 or 8 times 6 there are only two things to know.  1) A procedure to figure it out, which shows that you understand the “concept.”  2) What’s the answer?

It is important for students to understand the concept and to have a reliable procedure to figure out the answer to a math fact.  But there is no need for them to be required to use the laborious counting process over and over and over again!  Really, if you think about it, even though this student is doing his math “work” he is not learning anything. 

Math teaching strategy:  Go ahead and memorize those facts.

(It won’t hurt them a bit.  They’ll like it actually.)

Once students know the procedure for figuring out a basic fact, then they should stop figuring it out and just memorize the answer.  Unlike capitals and countries in the world, math facts are never going to change.  Once you memorize that 9 plus 7 is 16, it’s good for a lifetime.  Memorizing math facts makes doing arithmetic MUCH easier and faster.  Hence our tagline

Rocket Math: Because going fast is more fun!

Memorizing facts is the lowest level of learning.  It’s as easy as it gets.  But memorizing ALL the facts, which are similar, is kind of a long slog.  Some kids just naturally absorb the facts and memorize them.

Math teaching strategy: Find a systematic way for students to memorize.

A lot of students don’t learn the facts and keep counting them out over and over again.  They just need a systematic way of learning the facts.  Students need to spend as much time as necessary on each small set of facts to get them fully mastered.  If the facts are introduced too fast, they start to get confused, and it all breaks down.  Each student should learn at their own pace and learn each set of facts until it is automatic–answered without hesitation and without having to think about it.  This can be accomplished by everyone, if practice is carefully and systematically set up.  It should be done, because the rest of math is either hard or easy depending on knowing those facts.  And don’t get me started about why equivalent fractions are hard!

 

Math Teaching Strategies #2: Ensure math facts are mastered before starting computation

Rocket Math can make learning math facts easy.  But even more important it can make teaching computation easy too!  One of the first teachers to field test Rocket Math was able to teach addition facts to her first grade class, and then loop with them into second grade, where she helped them master subtraction facts as well.  She told me that because her second graders were fluent with their subtraction facts, they were ALL able to master regrouping (or borrowing) in subtraction in three days.  What had previously been a three week long painful unit was over in less than a week.  All of them had it down, because all they had to think about was the rule for when to regroup.  None of them were distracted by trying to figure out subtraction facts.

Math teaching strategy: Get single-digit math facts memorized before trying to teach computation.

When math facts aren’t memorized, computation will hard to learn, hard to do, and full of errors.

When math facts aren’t memorized, computation will be hard to learn.   I used to think computation was intrinsically hard for children to learn.  Because it was certainly hard for all of my students with learning disabilities.  But none of them had memorized the basic math facts to the point where they could answer them instantly.  They always had to count on their fingers for math.

When I learned more about the process of learning, I found out that weak tool skills, such as not knowing math facts,  interferes with learning the algorithms of math.  When the teacher is explaining the process, the student who hasn’t memorized math facts is forced to stop listening to the instruction to figure out the fact.  When the student tunes back into instruction they’ve missed some essential steps.  Every step of computation involves recalling a math fact, and if every time the learner has to turn his/her attention to deriving the math fact they are constantly distracted.  That interferes with the learning process.

When math facts aren’t memorized, computation will be hard to do.   Having to stop in the middle of the process of a multi-digit computation problem to “figure out” a fact slows students down and distracts them from the process.  It is easy to lose your place, or forget a step when you are distracted by the difficulty of deriving a math fact or counting on your fingers.  It is hard to keep track of what you’re doing when you are constantly being distracted by those pesky math facts.  And of course, having to figure out facts slows everything down.

I once stood behind a student in a math class who was doing multiplication computation and when he hesitated I simply gave him the answer to the math fact (as if he actually knew them).  He loved it and he was done with the small set of problems in less than half the time of anyone else in his class.  Children hate going slow and slogging through computation. Conversely, when they know their facts to the level of automaticity (where the answers pop unbidden into their minds) they can go fast and they love it.  That’s why “Because going fast is more fun!” is the Rocket Math tag line.

When math facts aren’t memorized, computation will be full of errors.  When I learned more about basic learning, I found out that the frequent student errors in computation were not simply “careless errors.”  I thought they were because when I pointed out simple things like, “Look you carried the 3 in 63 instead of the 6.” my students would always go “Oh, yeah.” and immediately correct the error.  If I asked them they knew that they were supposed to carry the number in the tens column, but they didn’t.

I thought it was carelessness until I learned that such errors were the result of being distracted.  Not by the pretty girl next to you, but by having to figure out what 7 times 9 was in the first place.  After going through the long thinking process of figuring out it was 63 they were so distracted that they carried the wrong digit.  Not carelessness but distraction.  Once students instantly know math facts without having to think about it, they can pay full attention to the process.  They make far fewer errors.

In short, don’t be cruel.  If you have any autonomy available to you, first help your students memorize math facts and then teach them how to do computation in that operation.  In other words, teach subtraction facts before subtraction computation.  If you help them get to the point where math fact answers in the operation come to them without effort, you’ll be amazed at how much easier it is to teach computation, for them to do it and at the accuracy with which they work.

Math teaching strategies #3: Teach computation procedures using consistent language

Improv can be entertaining, but it will frustrate students trying learn a procedure.

Much of math, and especially computation, is about learning a process or a set of procedures. [I am assuming you are practical enough to know that we cannot expect elementary aged children to re-discover all of mathematics on their own, as some people recommend.]

Learning a procedure means knowing “What’s next?”  If you ever learned a procedure (for example a recipe) you know that it is between steps, when you ask yourself, “What’s next?” that you need help from the written recipe.  Students are no different.  Just showing them what to do is usually not enough for them to be able to follow in your footsteps.  You need to teach them the steps of the procedure.  As with anything you teach, you are going to confuse your students if you do things in a different order, or with different words, or different steps.  What you call things, and some of how you explain yourself, and some of the sequence of doing the procedure is arbitrary.  If you are improvising you will do things differently each time and your students will be confused.  At a minimum you need  it written down.

Math teaching strategy: Use a script or a process chart to keep the instructions consistent.

We know a lot about how to help students learn a procedure.  We know we need to consistently follow the same set of steps in the same order, until students have learned it.  We know we need to explicitly tell students the decisions they must make while working so they know what to do and when, in other words, we have to make our thinking process overt.  We know we need to be consistent in our language of instruction so that students benefit from repetition of examples.  And finally, we know we need to careful in our selection of problems so that we demonstrate with appropriate examples how the new process works and where it does not work.

Guess what?  You can’t do all of that when you are improvising your instruction and making up the directions on the fly. To be able to do all that, you need a script and pre-selected examples.  Many teachers have been taught to use a chart of steps, posted in their classroom, to which they refer as they model a procedure.  The same effect can be achieved with a script, so that the teacher uses the same wording along with the same steps in the same order.  If you improvise, it won’t always be the same, which will confuse your students.

You have to learn when and how to make decisions.  Every math procedure involves looking at the situation and making decisions about what and how to do what needs to be done.  You have to know what operation to use, when to borrow, when to carry, where to write each digit and so on.  Because you as the teacher already know how to do the procedure, it is tricky to remember to explain your thinking.

Math teaching strategy: Teach a consistent rule for every decision students must make.

Good teaching involves first explaining your decision-making and then giving your students practice in making the right decision in the given circumstances and finally to make them explain why–using the rule you used in the first place.   First, you teach something like, “Bigger bottom borrows” to help students decide when to borrow.  Then you prompt them to explain how they know whether or not to borrow.  All of that should be asked and answered in the right place and at the right time.  A script or a posted process chart will help you remember all the decisions that have to be made, and what to look at to make the right one.  Without a script it is very unlikely that you will remember the exact wording each time.  You need a script to be able to deliver consistent language of instruction.

Math teaching strategy: Plan ahead to carefully choose the right examples. 

With some math procedures it is quite hard to choose the right examples.  The fine points can be obscured when the examples the teacher happens to come up with, are not quite right.  The examples may be an exception or handled differently in a way the procedure has not taught.  So for example borrowing across a zero is different than across other numerals so the numbers in a minuend must be chosen carefully rather than off the cuff.

Also, when teaching a procedure it is essential to teach when to use the procedure and when not to use that procedure.  It is important that the teacher present “non-examples,” that is, problems in which you don’t follow that procedure.  I have seen students who are taught, for example, borrowing, using only examples that need borrowing.  Then they turn around and borrow in every problem–because that is what they were taught.  They should have been taught with a few non-examples mixed in, that is, problems where borrowing wasn’t necessary so they learned correctly when to borrow as well as how to borrow.   Choosing teaching examples on the fly will often end up with more confusion rather than less.

If it bothers you to see students as frustrated as the one above, then find* or write out a script for teaching computation so that you can be consistent and effective.  Trust me, your students will love you for it.

* You may want to look at the “Learning Computation” programs within the Rocket Math Universal subscription.  Here are links to blogs on them:  Addition, Subtraction, and Multiplication.  These are sensible, small steps, clearly and consistently scripted so each skill builds on the next.

Math Teaching strategies #5: Separate the introduction of similar concepts

Teaching two similar concepts and their vocabulary terms at the same time creates confusion.

The classic example is teaching parallel and perpendicular on the same day.  The two concepts have to do with orientation of lines and the new vocabulary terms for them are similar.  So teaching them at the same time means some or many students will have the two terms confused for a long time.  That is known as a chronic confusion–possibly permanent.  They will know that orientation of lines is one of those two terms, possibly, but will be confused about which is which.  The predictable conversation with the teacher goes thusly:

Teacher:  See these two lines lines.  Are they parallel or perpendicular?

Student: I think they’re perpendicular.

Teacher: Well…

Student: No, wait! I know.  They’re parallel.

Teacher: Yes, you’re right.  I’m glad you’ve learned that.

In case you missed it, the above student did NOT know the correct term.  The student just knew it was one of two terms, but unsure as to which one.  So the student picked one and as soon as there wasn’t confirmation by the teacher, switched to the other term.  When you’re busy teaching it is easy to get fooled by that kind of response into assuming the students really did learn it.

Other examples abound in math.  Teaching numerator and denominator in the same lesson is common.  Teaching the terms proper fractions and improper fractions on the same day is another example.  Acute and obtuse angles are yet another pair of chronically confused concepts that are introduced simultaneously.

Math teaching strategies: Separate the introduction of similar concepts in time.

If you teach one concept and only one of the pair, there’s no cause for confusion.  It will still take a lot of repetition and practice for it to be cemented into memory, but students will be clear.  If they use the term, for example parallel a lot of times in conjunction with examples they will soon (in a couple of weeks) be able to recall.  However, you should pair the concept with non-examples of the concept.  Not the opposite necessarily but just not an example of the concept.

For example: For the picture to the right you would ask the students.

A “Are the two lines in item A parallel or not parallel?”   Ans: Not parallel.

B “Are the two lines in item B parallel or not parallel?”   Ans: Parallel.

C “Are the two lines in item C parallel or not parallel?”   Ans: Not parallel.

Then after a couple of weeks you could introduce perpendicular.  Again teach it on its own and then contrasted with non-examples until the vocabulary was clear. Probably for a couple of weeks.   Only then can you combine both terms in the same lesson.

Another advantage of this approach is that you have avoided the other common mistake.  Students sometimes come to the conclusion that all pairs of lines are either parallel or perpendicular.  This method of introducing the concepts helps them realize that there are non-examples of each concept, parallel lines and ones that aren’t as well as perpendicular lines and ones that aren’t as well.

 

Rocket Math: Can students really learn this way? (It seems too easy.)

At first, it may seem like the way Rocket Math presents the same simple facts over and over, is so easy it must be a waste of time.

       But like anything you learn, you have to start where it seems easy and then build up to where it is hard.  Rocket Math has been effective helping students learn their math facts for over 20 years.  It is designed according to scientifically designed learning principles, which is why it works, if students will work it.  Rocket Math carefully and slowly introduces facts to learn in such a way that students can achieve fluency with each set of facts as they progress through the alphabet A through Z.  Let me explain.
         Set A begins with two facts and their reverses, e.g., 2+1, 1+2, 3+1 and 1+3.  Dead simple, huh?  But in answering those the student learns what it is like to instantly “know” an answer rather than having to figure it out.  The student says to himself or herself, “Well, I know that one.”  The student learns he or she can answer a fact instantly with no hesitation every time based on recall and not figuring it out.  The game requires the student to answer the problems at a fast rate, proving that he or she knows those facts.  Once that level is passed the game adds two more facts and their reverses,.  The same process of answering them (and still remembering Set A) instantly with no hesitation every time.  When that is achieved, the game moves the student on to Set C, two more facts and their reverses.  Eventually, every student gets to a fact on which they hesitate (maybe one they have to count on their fingers), meaning they can’t answer within the 3 seconds allowed.  Mission Control then says the problem and the correct answer, has the student answer that problem, then gives two different facts to answer and goes back to check on the fact the student hesitated on again.  If the student answers within 3 seconds then the game moves on.
 
     In the Take-Off phase the student is introduced to the two new facts and their reverses.  That’s all the student has to answer.  But the student has to answer each one instantly.  If the student is hesitant on any of those facts (or makes an error) then they have to Start Over and do the Take-Off phase over again.  They have to do 12 in a row without an error or a hesitation.  Once the Take-Off phase is passed the student goes into the Orbit phase, where there is a mix of recently introduced facts along with the new facts.  The student has to answer up to 30 facts, and is allowed only two errors or hesitations. After the third error or hesitation the student has to Start Over on the Orbit Phase.  Once the Orbit phase is passed, the student goes on to the Universe phase, which mixes up all the facts learned so far and presents them randomly.  Again the student has to do up to 30 problems and can only hesitate on 2 or them or he or she has to start over.  But once the student proves that all of those facts can be answered without hesitation, the game moves on to the next level, introducing two more facts and their reverses.
      In the Worksheet Program, students practice with a partner.  In the Online Game the student practices with the computer.  In both versions of Rocket Math the students follow the same careful sequence and slowly, but successfully build mastery of all of the facts in an operation.  It’s hard work and takes a while, but we try to make it fun along the way.  It will work for everybody, but not everybody is willing to do the work.  At least, now you understand how Rocket Math is designed so it can teach mastery of math facts.

Dictating Sentences, do students need automaticity in spelling too?

Few teachers realize how similar spelling and math facts are.

Both spelling and math facts are tool skills. Tool skills are things which one needs to do academic work, tools you use to do other things.  The tool skills of spelling and math facts (like decoding) need to become so automatic that students don’t have to think about them.

If students have to think up the answer to math facts, it makes doing computation harder.  The process of figuring out a math fact distracts from the mathematics being done.  Similarly, if you have to stop and think of the spelling of a word (like the boy pictured above) while you are trying to write, it distracts you from thinking about what you are trying to write.  Students are more successful and better able to show what they know and better able to focus on learning when their tool skills have developed to the level of automaticity.

Daily practice develops automaticity.  Developing automaticity with math facts and with spelling requires a lot of practice.  Daily practice is best and a few minutes a day is optimal.  That is why Rocket Math is designed the way it is–to provide that daily practice.  So Dictating Sentences gives each member of the pair ten minutes a day of practice writing sentences composed of words they know how to spell.

Dictating Sentences is spelling with a twist.  Instead of spelling one word at a time, in Dictating Sentences (now part of the Universal Level Rocket Math Worksheet Program) students are asked to write an entire sentence from memory.  They work in pairs and their tutor has the student repeat the sentence until it is learned.  Then the student has to write the whole sentence from memory.  It turns out this is considerably harder than writing words on a spelling test, so it is challenging practice, and does a lot to help students develop automaticity with spelling.

Working in pairs.  As you know from Rocket Math practice, students enjoy working in pairs.  And when one partner has an answer key the practice can be checked and corrected.  Sound research shows that immediate correction and editing of misspelled words is the fastest way to learn the correct spelling, so that’s what we have the student tutor do.  After each sentence is written every word is checked and practiced again until it is correct.

Mastery learning. The program is structure so that all the words are learned to the level of automaticy.  Students keep working on a sentence until it can be written without any errors.  They work on the same lesson for as many days as is needed for them to spelling every word perfectly in all three sentences.  Each sentence persists for two or three lessons, so that the student is required to write it from memory and spell every word perfectly for several days in a row.

Earning points by being correct and going fast.  Students earn two points for every word that is spelling correctly the first time.  Every word on which there is an error is worked on until it too can be spelled correctly, earning one point.  The faster students go during their ten minutes, the more points they can earn.  Students graph the amount of points earned and try to beat their own score from previous days.  Teams can be set up and competition for the glory of being on the winning team can enhance the motivation.

Individual Placement.  There is a placement test.  Students begin at the level where they first make a mistake.  Student partners do not need to be at the same level, so every student can be individually placed at the level of success.

Choose a Learning Track for Online Game

Choose from ten Learning Tracks

In the Rocket Math Online Game every student needs to be started in one of the ten Learning Tracks.  A student’s Learning Track can be changed at any time**, but one must be chosen to begin with.

If you are entering the Student Login individually, you can use the pull down menu to select a learning track, as illustrated to the right.

The ten learning tracks are numbered as follows. If you are using the csv method of entry you’ll need to enter the number for the track.

  1. Addition 1s through 9s
  2. Subtraction 1s through 9s
  3. Multiplication 1s through 9s
  4. Division 1s through 9s
  5. Fact Familes (1 to 10) add and subtract, ex.4+5, 5+4, 9-4, 9-5
  6. Fact Families (11 to 18) add and subtract, ex. 8+7, 7+8, 15+7, 15-8
  7. Add to 20, example 13+4, 4+13,
  8. Subtract from 20, example 15-3, 15-12,
  9. Multiplication 10s-11s-12s,
  10. Division 10s-11s-12s.

You can click below to see a google document showing all the problems learned in each of the Learning Tracks.

Click to see the problems in the tracks.

Considerations, or what to choose when?

Begin with the basics.  The four basic operations are most important and typical expectations is one of those per grade level, so Addition in first, Addition then Subtraction in second, Multiplication, then go back to Addition and Subtraction in third, and Multiplication then Division in fourth grade, and then going back to get Addition and Subtraction if those haven’t been learned.  Make sure your student have worked through the expected basic operations for their grade level BEFORE doing any of the other optional Learning Tracks.

Another way to learn basic Addition and Subtraction Facts.  Learning in Fact Families is another order to learn. Fact Familes (1 to 10) add and subtract would be chosen in first grade.   Fact Families (11 to 18) add and subtract would be mastered in second grade.  You can choose this sequence instead of the basic addition and basic subtraction fact Learning Tracks.   Optionally, Fact Families is also a good way to review for students who have already learned the basic addition and subtraction facts in first or second grade.

Optional Learning Tracks. Add to 20 and Subtract from 20 are additional problems that the Common Core feels should be committed to memory.  They are composed of facts you can figure out if you know the basic 1s through 9s facts, but can be learned AFTER the basics are learned, if there is time in first or second grade.  They should not be assigned until after the student has mastered the basic 1s through 9s addition and subtraction facts.

After students learn the basic 1s through 9s multiplication facts, if there is time, they can move on to 10s, 11s, 12s.  After basic 1s through 9s  division facts are learned (and all the other basic operations are learned) then the 10s, 11s, and 12s are a good use of time.

 

**See “How to change Learning Tracks” in the FAQs and Directions document.