teaching

Are your students wary of working with integers?

Posted on by Dr. Don

Many students find integers confusing.  If you add a negative to a negative are you getting more or less??? Over the years different “rules” have been used to try to remember what should happen.  Rules such as “two negatives make a plus” or “opposite signs subtract.”  Whatever is used to try to remember, it interferes with a student’s ability to quickly and reliably get the answers without having to stop and puzzle it out.

I have posted a series of free lessons online (links below) that use a vertical number line to take some of the confusion out of the process.  Turns out there are a total of eight types of problems but all of them can be solved with the same process on the vertical number line.  Intuitively on a vertical number line, up is more and down is less.

(1) Mixed Integers Set A1 Positive add a positive

(2) Mixed Integers Set A2 Positive subtract a positive

(3) Mixed Integers Set D Negative add a positive

(4) Mixed Integers Set G Negative subtract a positive

(5) Mixed Integers Set J Negative subtract a negative

(6) Mixed Integers Set M Positive subtract a negative

(7) Mixed Integers Set P Positive add a negative

(8) Mixed Integers Set S Negative add a negative

Using the vertical number line there are two rules to learn.  Rule 1: When you add a positive or subtract a negative you go up on the number line.  Rule 2: When you subtract a positive or add a negative you go down on the number line.

So first thing to figure out is whether you’re going up or down.  Once you do that you simply make “bumps” going either up or down from where you start.  That gives you the answer without any uncertainty.  These lessons are quick (about 2 minutes) and identify a pattern of whether the answer is like the sum or the difference between the numbers.  Once students can recognize the pattern they can begin to answer fluently and without a struggle.

To help with the work of learning to quickly and easily recognize each pattern in Integers Rocket Math now includes a “Mixed Integers” program in our Universal Subscription.  (Click here to get a 60-day trial subscription for $13 –rather than the standard $49 a year.) Students use the vertical number line to work a problem. In this example: -6 minus (-4).  Then they have a set of problems with the same pattern they can orally answer without having to use the number line.

As with all Rocket Math programs there is a 3 minute practice session, with a partner.  Then the two switch roles.  Then the practice is followed by a one-minute test.  If the student can answer the problems without hesitations the level is passed.  If it is still difficult the student stays with that level a bit longer.  When a new pattern is introduced the tests will have a whole row of problems that are the same pattern. When that level is passed the next test will have two types of problems in each row.  The next level has 3 types, then 4 types in each row.  Then the problem types are mixed.  This way the student develops fluency in recognizing the type of problem and how to derive the answer quickly.

Rocket Math has a money-back satisfaction guarantee.  If you try this and find it isn’t everything you hoped, in terms of helping your students become fluent with integers, I’ll gladly refund your money.  I’m betting they’re going to love it.

 

Foolproof method for finding factors

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Knowing when you’ve found ALL the factors is the hard part.

Students have to learn how to find the factors of a number because several tasks in working with fractions require students to find the factors of numbers. Thinking of some of the factors of a number is not hard. What is hard is knowing when you have thought of ALL the factors. Here is a foolproof, systematic method I recommend: starting from 1 and working your way up the numbers. This is what student practice in the Rocket Math Factors program.

https://youtu.be/fDYMRfxtGIc

I have a white board type video lesson that explains this in 6 minutes. https://youtu.be/fDYMRfxtGIc

Bookmark this link so you can show it to your students.

How to find all the factors of numbers
Always begin with 1 and the number itself-those are the first two factors. You write 1 x the number.  Then go on to 2. Write that under the 1. If the number you are finding factors for is an even number then 2 will be a factor. Think to yourself “2 times what equals the number we are factoring?” The answer will be the other factor.
However, if the number you are finding factors for is an odd number, then 2 will not be a factor and so you cross it out and go on to 3. Think to yourself “3 times what equals the number we are factoring?” There’s no easy rule for 3s like there is for 2s. But if you know the multiplication facts you will know if there is something. Then you go on to four—and so on.

The numbers on the left start at 1 and go up in value.  The numbers on the right go down in value.  You know you are done when you come to a number on the left that you already have on the right.  Let’s try an example.

Factors Answers d

Let’s find the factors of 18.  (To the left you see a part of a page from the Rocket Math factoring program.)
We start with the first two factors, 1 and 18. We know that one times any number equals itself. We write those down.
Next we go to 2. 18 is an even number, so we know that 2 is a factor. We say to ourselves, “2 times what number equals 18?” The answer is 9. Two times 9 is 18, so 2 and 9 are factors of 18.
Next we go to 3. We say to ourselves, “3 times what number equals 18?” The answer is 6. Three times 6 is 18, so 3 and 6 are factors of 18.
Next we go to 4. We say to ourselves, “4 times what number equals 18?” There isn’t a number. We know that 4 times 4 is 16 and 4 times 5 is 20, so we have skipped over 18. We cross out the 4 because it is not a factor of 18.
Next we go to 5. We might say to ourselves, “5 times what number equals 18?” But we know that 5 is not a factor of 18 because 18 does not end in 5 or 0 and only numbers that end in 5 and 0 have 5 as a factor. So we cross out the five.
We would next go to 6, but we don’t have to. If we look up here on the right side we see that 6 is already identified as a factor. So we have identified all the factors there are for 18. Any more factors that are higher we have already found. So we are done.

Now let’s do another number.  Let’s find the factors of 48. 

We start with the first two factors, 1 and 48.  We know that one times any number equals itself.

Next we go to 2.  48 is an even number, so we know that 2 is a factor.  We say to ourselves, “2 times what number equals 48?”  We might have to divide 2 into 48 to find the answer is 24.  But yes 2 and 24 are factors of 48.

Next we go to 3.  We say to ourselves, “3 times what number equals 48?”   The answer is 16.  We might have to divide 3 into 48 to find the answer is 16.  But yes 3 and 16 are factors of 48.

Next we go to 4.  We say to ourselves, “4 times what number equals 48?”  If we know our 12s facts we know that 4 times 12 is 48.  So 4 and 12 are factors of 48.

Next we go to 5.  We might say to ourselves, “5 times what number equals 48?”   But we know that 5 is not a factor of 48 because 48 does not end in 5 or 0 and only numbers that end in 5 and 0 have 5 as a factor. So we cross out the five.

Next we go to 6. We say to ourselves, “6 times what number equals 48?”  If we know our multiplication facts we know that 6 times 8 is 48.  So 6 and 8 are factors of 48.

Next we go to 7.   We say to ourselves, “7 times what number equals 48?”   There isn’t a number.  We know that 7 times 6 is 42 and 7 times 7 is 49, so we have skipped over 48.  We cross out the 7 because it is not a factor of 48.

We would next go to 8, but we don’t have to.  If we look up here on the right side we see that 8 is already identified as a factor.  So we have identified all the factors there are for 48.  Any more factors that are higher we have already found.  So we are done.

“Knowing” means never having to figure it out

Posted on by Dr. Don

Most people, for example, know their name, by memory.

In a previous blog I discussed  What does CCSS mean by “know from memory?”    

A reader asked the following question:

This topic of “know from memory” is something I have been digging into as a special educator. I wonder what your thoughts are about whether certain accommodations from these “know from memory” standards would actually be modifying the curriculum?

For example, if we used “extra time to respond” and the student had to use their fingers or some other method to count, would they then not be doing the standard?

This relates to where I’m at in middle school math, but I think that it’s reflected in the continuum of the common core maths.

Thanks.

Dr. Don’s response: 

Actually, your example is very clear that it is not “knowing from memory.” You are describing “deriving from a strategy” or what I call, “figuring it out.” When you know it from memory, when you recall the answer, then you stop having to “figure it out.”

Knowing from memory and figuring something out are two very different things. I used to ask workshop participants to imagine sitting next to me in a bar and asking me for my name. What if, instead of saying, “Hi, my name is Don,” something different happened?  What if, like the man pictured above, I was puzzled and said, “Wait a second, I have it here on my driver’s license.” Most people would likely turn their attention elsewhere while wondering what kind of traumatic brain injury I had sustained! They would very likely say to themselves, “OMG, that man doesn’t know his own name.”

The purpose of the verbal rehearsal that is a daily part of Rocket Math is to cement these basic facts in memory. Then when a student says to themselves, “8 times 7 is,” the answer pops into their mind with no effort. It takes quite a bit of practice to achieve that. However, the ability to instantly recall the answers to basic math facts makes doing mathematical computation a relative breeze. It make seeing relationships among numbers very obvious. It makes reducing fractions and finding common denominators easy. That’s why the Common Core thinks “knowing from memory” is so worthwhile. It’s why I began promoting Rocket Math in the first place.

Do you know the active ingredient in Rocket Math?

Posted on by Dr. Don

Timed tests are not the important part of Rocket Math.

The “active ingredient” in the Rocket Math prescription, the thing that makes it work, is not timed tests.  Timed tests don’t actually teach and often don’t really help students develop fluency.  The usual timed tests of a random selection of all the facts can assess fluency in math–but they don’t work to develop it!

The “active ingredient,” the thing that makes Rocket Math effective, is verbal rehearsal.  When students practice with their partner the students read the facts and RECALL the answers from memory and say them aloud.  That verbal rehearsal is what cements them into memory.  Reading the fact and recalling the answer from memory strengthens the neural connection.

Why do we give the daily tests in Rocket Math?  Not to teach, but only to assess whether the facts introduced thus far have been learned well enough for the student to have new facts added to what they are learning.  Individual students learn at different rates.  Some students need only a couple of days of practice to memorize two new facts while others may need several days.  The purpose of the daily tests is just to see if the student needs more practice time, or is ready to “swallow” some more facts.

As I note in my basic training presentation, “It’s like feeding mush to a baby.  You have to make sure they have swallowed the last mouthful before you give them more.”   See an explanation in this You Tube video in our Rocket Math channel: https://youtu.be/J8cWSDG0Di8

two students practicing rocket math facts with a quote "8 times 7 is 56"

Keeping track of progress in Rocket Math

Posted on by Dr. Don

Which students are progressing as fast as they should be in Rocket Math?

And how fast should they be progressing, anyway?

Over the years of helping teachers and schools implement Rocket Math I have learned that a complete laissez-faire attitude about student progress can mean that some students get stuck for weeks on the same sheet.  Needless to say, students who get stuck, come to hate Rocket Math.  When this happens, those students don’t get through all the operations they should learn.  So we need to intervene, and give them more help.  It turns out that some students need more practice, sometimes two or three times more practice, to learn the facts than their peers.  To get such students through one operation a year means they have to have extra practice sessions scheduled in each day.  Here’s a link to a blog about how to provide extra help.

But which students need extra practice sessions?   Under Resources/Educator Resources I’ve created two versions of a tool that can help.

Whole Class Excel Rocket Math (2 operations in a year) Aimline.  This is pictured to the right.  It is needed for 2nd grade and 4th grade and up when students need to finish one operation and do a second one in a year.  The expectations needed to pass two operations in one year are basically that students should pass two sets each week.  If they have studied some the year before, they will be able to pass sets in the first operation at a quick pace.  For example if they have done much of Rocket Math Addition in first grade, in second grade they should be able to pass those addition sets again in a day or two.  That will put them ahead of the expectations and they should have a plus by their name most of the year.  Conversely, if they are not able to pass sets quickly, (see the students highlighted in yellow) they will get a minus by their name and should start getting extra sessions scheduled daily.

How does the Excel Aimline work?

Please note: The pictured EXAMPLE Rocket Math Excel Aimline is available from the link or in the Resources/Educator Resources page for you to download. 

Take the blank template and save it for next year.  Then fill out one for this year.  Look at a calendar and on row 4 enter the month and on row 5 enter the starting day of each week in the school year.  so each column numbered 1 through 36 will correspond to a week in your school year.  In row 7 you see the green expected set to be passed by the end of that week.  At the end of week 1 we expect that students will have at least passed Set A.   By the end of week 2 they should have passed Set C to be on pace to finish two operations in a year.

Entering student names.  Starting in row 10 you enter the student names in column B.  This class only has ten students, but I’m guessing yours probably has more!   Cool thing about excel is you only have to enter those names once.  And if you’re really good you can freeze that column so you can easily see it later in the year.

Entering weekly information.  Each week grab all the student folders and for each student enter the highest set they have passed.  You can see that from the Rocket Chart on the outside of the folder, so you don’t even have to open the folders.  If the letter they have passed is equal or higher than the green set expected at the top of the column for that week, then put a plus by the letter they have passed.

Look at Alvin Ailey at the top of my class list.  Week 1 he had passed both Set A and B, so I wrote “B” in his square.  I put a plus because it is exceeds the expected level for the first week.  By the second week he had also passed Sets C and D.  Only up to “C” is expected,  so I wrote “D” and also gave him a plus.  Alvin is rocking it!

Look at Cindy Crawford a little further down the class list.  Week 1 she had passed Set A, so I wrote an “A” in her she got a plus because she met the expectation.  But by week 2 she had only passed Set B, when C is expected to be passed, so I wrote “B” in her square, with a minus indicating she is below expectation.  Now I highlighted her square yellow, but that’s kind of advanced so you don’t really have to do that.  Only Excel experts can do that, although it really makes it easy to pick out who needs help.  We can see that Cindy continues to make slow progress and continues to get minuses.  She needs to have extra practice sessions scheduled to finish two operations this year.  That pace is fine for one operation per year, but not two.

Look down at Gary Grummond.  He didn’t pass even Set A by the end of the first week so I wrote “np” in the first square.  He continues to make progress the next few weeks, but not fast enough to complete two operations in a year.

Row 8 Fraction of students meeting expectation.    After entering all the students for the week you can see how you are doing overall in your class.  Make a fraction with the numerator being the number of students who are meeting the expectation over the denominator of the number of students in the class.  You want a high fraction nearer to 1.

If that fraction falls below 70%, meaning more than 30% of your class is not on track, then you should institute a class-wide intervention.  Either add an extra practice session each day, or see if there is room to improve the quality of practice.  See these blogs and posts about how to monitor for the quality of practice.

Whole Class Excel Rocket Math (1 operatipon per year) Aimline.   In grades 1 and 3 where students are expected only to complete one operation in a year, you can use this Excel Aimline.  The expectations needed to pass one operations in a year are basically that students should pass one set each week.   Everything else about how you use the excel form is the same.  Note that if you want students to do two operations in the year (for example both subtraction and multiplication in 3rd grade) then you would use the two operation aimline.

 

Learning Addition Computation quickly and easily

Posted on by Dr. Don

Rocket Math adds something new: Addition—Learning Computation

After becoming fluent with addition facts the best way for students to retain the knowledge of those facts is by doing addition computation. Rocket Math has added a new program to the Universal Subscription that teaches addition computation.  If students have not been taught addition computation, this program breaks it down into small, easy-to-learn steps that are numbered in a teaching sequence that leaves nothing to chance.  There is an placement assessment that can be given to figure out where the student should begin in the sequence.

Note that the number for each skill gives the grade level as well as indicating the teaching sequence.  Skill 2a is a 2nd grade skill and after skill 2f is learned the next in the sequence is skill 3a.  The sequence of skills is drawn from M. Stein, D. Kinder, J. Silbert, and D. W. Carnine, (2006) Designing Effective Mathematics Instruction: A Direct Instruction Approach (4th Edition) Pearson Education: Columbus, OH.

(1b) Adding 1-, or 2-digit numbers; no renaming

(2a) Adding three single-digit numbers

(2b-c) Adding 3-digit numbers; no renaming

(2c) Adding 3-digits to 1 or more digits; no renaming

(2d) Adding three 1- or 2-digit numbers; no renaming

(2e) Adding two 2-digit numbers, renaming 1s to 10s

(2f) Adding 3-digit numbers, renaming 1s to 10s

(3a) Adding a 1-digit number to a teen number, under 20

(3b) Adding two 2- or 3-digit numbers; renaming 10s to 100s

(3c) Adding 3-digit numbers; renaming twice

(3d) Adding three 2-digit numbers; renaming sums under 20

(3e) Adding four multi-digit numbers; renaming, sums under 20

(4a) Adding a 1-digit number to a teen number, over 20

(4b) Adding three 2-digit numbers, sums over 20

(4c) Adding four or five multi-digit numbers, sums over 20

For each skill there is a suggested Teaching Script giving the teacher/tutor/parent consistent (across all the skills we use the same explanation) language of instruction on how to do the skill.  The script helps walk the student through the computation process.  For the teacher, in addition to the script, there are answer keys for the five worksheets provided for each skill.

Each worksheet is composed of two parts.  The top has examples of the skill being learned that can be worked by following the script.  After working through those examples with the teacher the student is then asked to work some review problems of addition problems that are already known.  The student is asked to do as many as possible in 3 minutes—a kind of sprint.  If all is well the student should be able to do all the problems or nearly all of them, but finishing is not required.  Three minutes of review is sufficient for one day.

There are five worksheets for each skill.  Gradually as the student learns the skill the teacher/tutor/parent can provide progressively less help and the student should be able to do the problems without any guidance by the end of the five worksheets.  There are suggestions for how to give less help in the teaching scripts.  Thumbnail previews can be found here.

Learn to add and subtract in first grade with fact families

Posted on by Dr. Don

A number of math programs around the country introduce math facts in families.  Now Rocket Math does too!

A fact family includes both addition and subtraction facts. You can see to the right 25 examples of fact families such as Set A; 3+1, 1+3, 4-1 & 4-3.  The sheet shows the sequence of learning facts in the new Rocket Math  program Fact Families 1s-10s (+, -).  Each set that students learn from A to Y adds just one fact family to be learned, so it isn’t too hard to remember.  (That’s the Rocket Math secret ingredient!) 

Learning math facts in families, is gaining in popularity these days.  Logic suggests that this would be an easier way to learn.  However, the research is not definitive that this is easier or a faster way to learn facts than separating the operations and learning all addition facts first and then learning all subtraction facts.  But learning in fact families is a viable option, and I wanted to have it available for Rocket Math customers.

Flash news!! Someone looking for a master’s or doctoral thesis could do a comparative study of students using the fact families vs. the separated facts in Rocket Math. This could easily be a gold standard research study because you could randomly assign students to conditions within classrooms–the routine is the same for both–just the materials in their hands is different!  Just sayin’…

I separated out the 1s through 10s facts from the 11s-18s, because this seemed enough for one program.  It would be a good and sufficient accomplishment for first grade.  I have heard that some first grades prefer to keep the numbers small but to learn both addition and subtraction–so this program accomplishes that.

I added Fact Families 1s-10s (+, -) to the Universal subscription in April of 2017 bringing the total number of programs in the Universal subscription to 14 (the basic four operations and ten more!).  By the fall of the 2017 school year I should have the rest of the Fact Familes in addition and subtraction available.  [In time for you to do that gold standard research study!]  The rest of the addition and subtraction fact families, which students could learn in 2nd grade, would be the Fact Families 11s-18s (+, -).  As always, new programs are added to the Universal subscription without additional cost as soon as they are available.

I most sincerely want students to be successful and to enjoy (as much as possible) the necessary chore of learning math facts to automaticity. Please give me feedback when you use this new program, Fact Families 1s-10s (+, -),  as to how it goes for the students.

Why is a gifted student having trouble with Rocket Math?

Posted on by Dr. Don

Question: Hi, Dr. Don! Just had a question recently from a parent of a gifted child whose son is having a lot of difficulty doing Rocket Math! He understands almost everything conceptually in math (in the 99% on national testing) but he is not being successful working with a partner on his math facts. Have you had this problem in other places? I’m not sure if the problem is he really can’t focus on the facts, he’s stubborn and doesn’t like details (big picture thinker), etc. He’s a very social kid so the partnering doesn’t seem to be the problem. I would greatly appreciate any suggestions you might have that I could give this mother. She says that he is fine at home doing his facts with her without a timer. But I don’t like the idea of excusing any student from doing this valuable practice. Thanks for your thoughts. Linda

Answer: I’ve blogged a bit on some of these issues elsewhere on the Rocket Math website, but let me try to be more specific here. First, gifted kids are stunned to find out that they have to work hard to memorize math facts. They probably need three or four days of practice—which to them seems like failure.  They are like an athletic kid who excels easily at every sport but finds he needs to work out with weights as much as a klutz to get to be able to lift heavy weights—his natural talent doesn’t help in this instance. So kids who’ve never had to work to learn things before, really are annoyed by having to practice several days in a row.  But it is really good for them!

How is mom practicing with him at home? Can she video him doing the test “untimed?”  If the child is “writing facts” and “without a timer” then he may be figuring out facts over and over—but is not getting to instant recall. That’s why the oral peer practice is so critical—if there is even a slight hesitation the child is to repeat the fact three times, back up three problems and come at it again—until the answer comes with no hesitation. There is a fundamental difference between instant recall of facts from memory and strategies to come to the answer by thinking it through. My parent letter addresses how to practice.  On the other hand, if the student is able to write the answers to math facts at a fast enough rate to complete 40 problems in a minute, but only when he thinks he is not being “timed” then he needs to learn how to do the same thing when he is being timed.

If he is not learning with the daily practice, we have to ask, “Why not?”  Social kids sometimes socialize instead of practicing. Social kids also can convince their partner not to do the correction procedure. Or they just say the answers instead of the whole problem and the answer. Any of those things would result in not successfully learning the facts. The teacher would need to monitor the quality of the practice. My experience has been that when students are “stuck” or “having difficulty” even just one session of practice done the right way rigorously (with me) and they suddenly improve enough to pass or to recognize they can pass the next day with another session of rigorous practice.

Last of all, sometimes the writing goals are off because of some glitch in how you gave the writing speed test.  So the student might know the facts well enough but not be able to write them fast enough to pass the tests.  If the student can answer 40 facts in a minute in the current set (just saying the answers without having to say the problems) then the facts are learned to automaticity—and the goal in writing should be lowered to whatever the student has done to this point.

Hope this helps. You are right not to excuse this student from learning math facts to automaticity. He might be a stellar mathematician someday if he learns his facts well enough that math computation is always easy for him. If math computation remains slow or laborious he won’t like it enough to pursue it as a career.

Rush help to those who need it with an aimline

Posted on by Dr. Don

The sooner you provide extra help the easier it will be to catch them up.  

How can you know when students need help to meet expectations?  Use the graph above, which is available from the Educator’s Resources page or here: One Semester Aimline.  It is also available in the basic subscription site, Forms and Information Drawer as an optional form. It is an “aimline” for finishing an operation (Sets A-Z) in one semester.  Schools that don’t start Rocket Math in first grade need students to finish addition in the first semester of 2nd grade and subtraction in the second semester.  This means that students who get stuck on a level for even a week need to be helped.

If you indicate on this graph the week in which the student finishes each set in Rocket Math you can tell if the student is making enough progress, or if he/she needs to be getting extra practice sessions each day. If the student is working on a set above the line of gray boxes or on the line then progress is adequate–they are on track to finish the operation by the end of 18 weeks of the semester.  But if the student is working on a set that is below the line that means he/she needs intervention.

In the example above the student whose progress is shown in red is above the aimline.  That student has been passing at a rate that means he or she will finish the operation by completing Level Z by the end of the semester.  That student does not need any extra intervention.  In the example above the student in blue is falling behind.  By the fourth week that student has only passed Level C and so he needs to have extra help.

The first step would be to ensure this student has a good partner and is practicing the right way.  Sometimes students don’t stay on task or do not listen and correct their partner.  If hesitations are allowed (while the student figures out the answer) and not corrected the student will not improve.  Fix the practice in class first and see if the rate of passing improves and the student starts to get up to the aimline.

The second step is to include this student in a group of students who get a second practice session each day.  They would work in pairs and do another Rocket Math session each day.  Whether or not they take tests is unimportant.  What is important is that they do the oral practice with a partner who corrects their hesitations as well as their errors.  This could be done by a Title One teacher or assistant or a special education teacher or assistant.  It should only take ten minutes.

Another step is to involve parents if that’s possible.  Another practice session (or two) at home each evening would make a big difference.  Parents will need to know how to correct hesitations, but there’s a parent letter in the Forms and Information drawer for that.  Also note that siblings can do this practice as well, as long as they have an answer key.

You will be pleasantly surprised at how an extra few minutes a day of good quality practice can help students progress much faster at Rocket Math.  The sooner you intervene, the easier it will be for the student to catch up.

NOTE: There is an aimline for finishing one operation in a year.  It is also in the Forms and Information drawer and on the Educator’s Resources page of our website.  If you follow recommendations and do addition in first grade, subtraction in second, and multiplication in third you can use that aimline.  It won’t require intervening on so many students.

 

 

What about students who can’t pass in 6 tries?

Posted on by Dr. Don

A teacher writes:

Help! I’m feeling bogged down in Rocket Math. I have some students who have been working on the same sheet for over 10 times and are no closer to passing. What am I doing wrong?

Dr. Don answers:

The problem could be one of several things.  You have to diagnose what it could be.  I am assuming you have students practicing orally in pairs, with answer keys, for at least two minutes per partner every day (as shown in the picture above).  I am assuming you already have students, who do not pass, take home the sheet on which they didn’t pass and finish it as homework and practice with someone at home.  The extra practice session at home each day can be a big help and the students should be motivated to do that.   If this is the case and you still have a problem, below are two possible things that may be needed.

(#1) Need to improve practicing procedures.  Pick one of the students who is stuck and be that student’s partner while they practice orally.  Make sure they are saying the whole problem and the answer aloud so you can hear what they are saying.  Correct even any hesitations, not just errors.  Correct the student by saying the correct problem and answer, having them repeat the correct problem and the answer three times, then back up three problems and move forward again.

Diagnosis.  If, after practicing with you, the student does much better on the one minute timing and passes or nearly passes (this is what I usually found) then you know the problem is poor practicing procedures.  If your work with the student makes no difference (they don’t do better on the one-minute timing) and they seem equally slow on all the problems then it is not practicing procedures at fault.  Try #2

Solution:  Monitor your students closely during oral practice to see if they are all following the correct practice procedures.  If you have quite a few students who aren’t practicing well you may need to re-teach your class how to practice.  [Note: Even if they know how to do it but aren’t doing it right, treat it as if they just don’t know how to to do it correctly.]  Stop them and re-do the modeling of how to practice and how to correct for several days before allowing them to practice again.  If your students haven’t been practicing the right way, they won’t be passing frequently, and they will be unmotivated.  You have to get them practicing the right way so they can be successful and so they can be motivated by their success.

Solution:  If you have poor practicing with only a handful of students you might assign them to more responsible partners and explain to them that they need to practice correctly. During oral practice monitor them more carefully the next few days to be sure they are practicing better and passing more frequently.

(#2) Need to review test problems also.  The problems practiced around the outside are the recently introduced facts.  The problems inside the test box are an even mix of all the problems taught so far.  If there has been a break for a week or more, or if the student has been stuck for a couple of weeks, the student may have forgotten some of the facts from earlier and may need a review of the test problems.

Diagnosis.  Have the student practice orally on the test problems inside the box with you.  If the student hesitates on several of the problems that aren’t on the outside practice, then the student needs to review the test items.

Solution. If you have this problem with quite a few students (for example after Christmas break) then have the whole class do this solution.  For the next three or four days, after practicing around the outside, instead of taking the 1 minute test in writing, have students practice the test problems orally with each other.  Use the same procedures as during the practice—two minutes with answer keys for the test, saying the problem and the answer aloud, correction procedures for hesitations, correct by saying the problem and answer three times, then going back—then switch roles.   Do this for three or four days and then give the one-minute test.   Just about everyone should pass at that point.

Solution.  If you have this problem with a handful of students, find a time during the day for them to practice the test problems orally in pairs.  If the practice occurs before doing Rocket Math so much the better, but it will work if done after as well.  They should keep doing this until they pass a couple of levels within six days.

If neither the first or the second solutions seem to work, write to me again and I’ll give you some more ideas.