Author: Dr. Don

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.

A screenshot of Rocket Math's beginning integers program where students learn through vertical graphs.A Vertical Number line is more intuitively obvious for learning integers.

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

 

Two rules to learn: when to go up and when to go down.

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 the 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 three “Integers” Learning Tracks in our Worksheet Program Universal Level Subscription.    (Click here to get a 60-day initial trial subscription for less than the standard full-year subscription.)

Screen shot of Rocket Math's integers program list.

Learn adding and subtracting separately or mixed.

The first integers learning track, Learning to Add Integers, is limited to adding integers.  In the above list of lessons, the adding lessons are numbers 1, 3, 7, and 8.  The second integers learning track, Learning to Subtract Integers, is limited to subtracting integers and teaches the processes shown in lessons 2, 4, 5, and 6.  The third learning track, Mixed Integers Drawer combines all 8 processes into one learning track.  If students are likely to have issues or begin to find the Mixed Integers lessons difficult, have them do the separate operation first.

In the Rocket Math Integers lessons, students use the vertical number line to work a problem. A screen shot of Rocket Math's subtracting integers worksheet.In this example: -2 minus (-3).  They use a rule and then apply it to the number line to find the answer. Then they have a set of problems with the same pattern they can orally answer without having to use the number line.

Students practice with a peer partner

As with all Rocket Math programs, there is a 3-minute practice session, with a partner.  The partner who is checking has the answer key and corrects all errors immediately.  Then the two switch roles.  Then the practice is followed by a one-minute test.  If the student can answer the problems without hesitation the level is passed.  If it is still difficult the student stays at 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, for 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.

 

More or better practice: improve the quantity or the quality of practice

Posted on by Dr. Don

If student progress slows, you need to improve or increase practice.

Students need to practice daily to develop math fact fluency.  When students are seeing regular success in Rocket Math, they are motivated and want to do Rocket Math every day (if not more.)  This is how it should be.  Students love Rocket Math when the implementation is being done well enough so they are passing every few days.  If they start to complain about doing Rocket Math, then something is amiss–because they aren’t making enough progress to be motivated.  You need to correct your implementation BEFORE that happens.

Students should pass a level in no more than 6 days.  That’s the reason there is room for only six “tries” on the Rocket Chart.  If any of your students are going beyond six “tries” without passing, there needs to be an intervention.

When students don’t pass regularly, they get discouraged.  Teachers need to intervene to help students make regular progress. They don’t need to find a different way to practice like flashcards or something else.  They just need more practice or better quality practice.  For any student who is not passing in six days, the teacher or parent needs to either improve the quality of their practice or the amount of their practice–or possibly both.

BETTER: Intervene to improve the QUALITY of practice.

You can check on the quality by observing each student as he or she practices with the partner. Monitoring carefully during practice is the key! 

  • Is the student saying the whole problem and the answer aloud and loud enough for the partner to hear?
  • Is the partner correcting hesitations and correcting the right way?
See the top four questions on the Rocket Math 100 Point Observation form.  
  • You might have to change a struggling student to be paired with a more conscientious partner.
  • You might have to re-teach your class how they should be correcting hesitations- by requiring them to MODEL the correction procedures.
  • You may need to explain how important correcting hesitations is, and why it is helping your partner, not punishing him or her.
  • You might have to reward or recognize students who actually do corrections the right way with public praise or points or tickets, etc

MORE: Intervene to increase the QUANTITY of practice.

Some students need two practice sessions each day, what football teams call “2-a-days!”

If you see that students are practicing the right way, but still not making good progress, then they will need extra practice sessions.  Note that you can add the extra practice sessions without adding tests.  Just the oral practice is what is needed.
Don’t do marathon session though!  Unfortunately, you can’t just extend the time students practice much beyond three minutes per partner or they won’t stay on task.  But if you provide two or three sessions of three minutes in length during the day, the students will progress much faster.  Read “Motivating by creating success.”  Students who get extra services from Special Education or Title personnel will likely need and benefit from an extra practice session with them every day.
An intervention tip: Do an extra session daily where students can practice the test items (inside the box) orally as well.  This could make a big difference.
If students are succeeding and passing a level every few days, just the recognition of that on their Rocket Chart is plenty of motivation.  But when they aren’t passing they become discouraged.  Often teachers will change their rewards to boost motivation for passing levels in Rocket Math.  I think that’s great and we have a bunch of ideas on how to boost motivation. But, if students don’t think they can succeed it is very difficult to motivate them.  Therefore, your first thing to address is their level of success–by improving either the quality or the quantity of their practice.

***  Motivation is composed of the incentive and the belief that it can be done.***

Dr. Don from Rocket Math watches the first Rocket Math app user complete math facts test

Four star rating for Rocket Math Apps

Posted on by Dr. Don

Rocket Math App received 4 Stars!

App Names: Rocket Math Add at Home, Add at School, Multiply at Home, and Multiply at School

Developer’s name: Rocket Math, LLC

App Link :

https://itunes.apple.com/us/app/rocket-math-multiply-at-home/id1048024368?mt=8

Primary School Apps (5-7 Years)

Educational App Store Review

Rocket Math is an offshoot of an existing programme for schools designed to increase children’s speed and fluency in answering simple arithmetic. This app encourages frequent short sessions and is supported by plenty of information explaining its purpose and methods.

The purpose of Rocket Math is to build what its developer terms “automaticity” in arithmetic. A fluent reader does not need to decode simple and frequently encountered words letter by letter. The same can be true for frequently encountered arithmetic.

When automaticity is achieved in arithmetic the answers are available in an instant. The advantages of this, beyond speed, are that it leaves more of the person’s mental processes available for other aspects of the problem. If a person does not have to think about achieving simple arithmetic answers, he or she can concentrate on the more complex and lengthier aspects of a problem.

Rocket Math the app follows on from a well-established programme of the same name based on traditional written resources. Repeat practice and a steady increase in the breadth of the covered arithmetic are at the heart of its methods.

Children are taken through a series of stages in which they are faced with a rapid succession of arithmetic questions. Remember, the purpose of this app is to build fluency in frequently encountered arithmetic problems, not complex ones. As such, the questions will be simple ones and, at first, until the breadth expands, there will be little variation in them. Only three seconds is allowed per question so, for some children, developing enough fluency to progress will be difficult but others will thrive on the challenge.

Answers are given by typing them onto a built-in number pad. The app is simple to use and looks attractive. Its space-travel styling and theme add a game-like feel although it is not a game. Speech provides a response to incorrect answers and provides encouragement between levels. It all works very well and provides the exact type of practice that it promises.

An unusual but useful feature is that the app enforces its little-and-often recommendations by insisting on a thirty-minute break after 5 minutes of play. As multiple sessions are likely to yield better results than a single, marathon session, this is an excellent feature that will prevent children from relying on a last-minute catch-up rather than a steady engagement with the app. This, combined with a useful breakdown of each child’s performance in the student report screen, provides reassurance to adults that their children are making the best possible use of the app.

A family of apps is available and potential buyers should think about which they need. Two of the apps cover addition and subtraction and two cover multiplication and division. Your choice here is obviously dependent on what aspect you would like to cover.

The remaining choice is between a school and a home version. They are identical in functionality except that the home version is free to download with a lengthy trial period. The school version has a flat, one-off, fee. Prospective teachers would still be wise to download the home version first so that they can appraise the app’s suitability.

If they choose to utilise the app within their school then buying the school version will be a simpler process than the in-app purchase of the home version. It will also allow schools to utilise the volume purchasing programme whereby they can receive a discount for buying twenty or more of the same app.

Parents will be pleased to see that the app caters for up to three children. As each child engages with the app, parents can check to see how they are performing and offer help, encouragement or rewards as they see fit.   Some useful background information on the app’s purposes and usage are provided within the app itself and a more comprehensive overview of the Rocket Math ethos is available on the developer’s website.

All of the Rocket Math apps provide a learning opportunity that is tightly focused on realising their goal of improving children’s arithmetic fluency. As such, if this is a goal that you also share, you will find them good value and useful apps.

How to reset your Rocket Math password

Posted on by Dr. Don

Four steps to get back into your account with a new password

There are 4 steps to get logged in if you haven’t done so since August 2017, or if your password doesn’t seem to work.  We have changed the look and location of the login screen.  You can access it from the top of the Rocket Math home page.

Step 1: Get to the login screen and click on “Reset Password.” 

You can click on “Teacher’s Subscription” on the blue bar, or hover and pull down to “Login,” or click on “Subscriber Account” on the orange bar.  All of them will take you to the “Login to your Account”  screen pictured here. (We had to change everyone’s password in August with the new system, so your old password won’t work, so step one is to change it.)
 The good news is all you have to do is click on Reset Password and it will take you to a screen where you can request a Password Recovery email.
P.S. You don’t even have to enter your email address on this screen–but you probably already did, so don’t worry about it.
  

Step 2: Request a password reset.


The Reset Password request asks you to tell the system where to send the Password Recovery email.  So fill in that box with your email address and then hit the button “Send me the Password Recovery email.”

 

 

 

Step 3: Open the email and Reset your Password.

Look for and open the Rocket Math: Password Recovery email.
You’ll get (pretty much instantly, so you don’t have time to go refill your coffee) an email entitled Rocket Math: Password Recovery that looks like this.  It gives you a link to go to a place where you can enter a new password.
 
P.S. Hint: This new system doesn’t know your old password, so you can use it again, which I highly recommend, if is is one you can remember.

Step 4: Go back to the “Login to your Account” screen and login.

Now you go back to the Rocket Math home page and click on “Teacher’s Subscription” on the blue bar, or hover and pull down to “Login,” or click on “Subscriber Account” on the orange bar.  All of them will take you to the login screen where you enter your email (as username) and new password.

Why should you renew your Rocket Math Worksheet subscription?

Posted on by Dr. Don

Reason #1 to renew: So we can be here for you.

Your subscription enables Dr. Don and our team to be available to help you with Rocket Math.  We can be here to answer your questions, help you with your implementation, provide customer service at assistance@rocketmath.com and to continue to expand our offerings.
Every day we correspond with and often get to talk with customers who have questions and need help. We have added programs such as Add to 20, Subtract from 20, Fact Families, Skip Counting and others to the Worksheet Subscription. (Check out the list on this link.) We are quite excited about the Learning Computation programs for addition, subtraction, multiplication and division.  Additionally, we have added tools such as the classroom wide aimlines in Excel to keep track of the progress of your whole class.  Most exciting of all, I have developed the Online Tutor that students will be able to use at home and at school with one log-in. Your subscriptions make all of that possible.  Thank you.

Reason #2 to renew: It will extend your permission to copy. 

The second reason to renew is that your subscription gives you “permission to copy” the materials only for a limited time.  After the subscription expires, permission to copy the materials also expires (it is no longer granted).  As you can see, the footers on our materials now show your name and the expiration date.  Don’t embarrass yourself by continuing to print these materials after your subscription has expired.  In order to continue printing and copying the Rocket Math worksheets, I ask that you please renew your subscription.

Reason #3 to renew: Access the virtual filing cabinet.

The third reason to renew is so that you continue to have access to the Rocket Math filing cabinet on the web.  New and updated materials are constantly being added to the filing cabinet. The materials now number in the thousands of pages!
 You can much more easily print from the website filing cabinet, than you can from a paper master copy.  You can print from home and even print from your phone.
Worksheets are updated in the filing cabinet.  When anyone finds an error in one of the thousands of worksheets, I can change it the same day in this virtual filing cabinet.  When anyone asks for a new form, I can share it with everyone instantly.

How to access (get into) my Worksheet subscription

Posted on by Dr. Don

Access your Worksheet subscription by logging in where it says  “Worksheet Subscription,” (outlined in yellow.)  It will take you to the login page you are seeing here, or you can click this link now https://www.rocketmath.com/members/login.

If you can’t remember your password you can hit our handy “Reset Password” link (outlined in red) to change it.  That will ask you for your email.  After you enter it you can send yourself an email to change your password.

** Here’s a hint: we don’t mind if you “reset” your password to what you thought it was in the first place, even if that was what you had previously, we won’t tell you that you used that one already. In other words, you don’t really have to change it. 

If you still can’t get in, try the reset access button at the bottom of the page (outlined in green.)

Once you login you should be taken straight into the Rocket Math File cabinet (pictured to the right).  You can open drawers and print files right from here.  Note the drawers that are part of the Basic subscription are labeled in blue.  The red-labeled drawers are only accessible to those with a Universal subscription.

You can get to your account (to upgrade or renew or change something) by clicking on the “Subscription Manager” link (outlined in yellow).

Be sure to “Logout”  (outlined in red) when you’re done in the filing cabinet.

If your Rocket Math subscription has expired

Posted on by Dr. Don
What if your subscription to the Rocket Math “filing cabinet on the web” has expired?

If you are still using Rocket Math, please consider renewing your subscription now.  

 

I think subscriptions that renew automatically, even when you aren’t using them, are a rip-off, so we don’t use them.  With Rocket Math you will need to take action to renew your subscription.

If you can’t log-in to the page shown below, here is how to reset your password. 

How to Renew your subscription–in 2 steps.

1.  Click into the Subscription Manager page.

Once you are logged into your account you’ll see the blue header and in the center (outlined in yellow in the picture) you’ll see “Subscription Manager.”  Clicking on that will take you to your account page.

2.  Click on the Renew Subscription button. 

Your account page will look like this. The top bar has tabs including one to Renew Subscription.  Click on that and you can choose which type of  subscription you would like (Basic or Universal) and what size (individual, 3 teachers, 6 teachers or Whole School) and then choose your method of payment (credit card, PayPal, or Purchase Order).

 

 Thank you for your support.

Dr. Don

Rocket Math: Because going fast is more fun.

 

Learning subtraction computation–easily and confidently

Posted on by Dr. Don

In 18 easy-to-manage steps!

Rocket Math Universal Subscription now includes Subtraction–Learning Computation.

After becoming fluent with subtraction facts the best way for students to retain the knowledge of those facts is by doing subtraction computation.  If students have not been taught subtraction computation, Subtraction–Learning Computation breaks it down into 18 small, easy-to-learn steps that are numbered in a teaching sequence that leaves nothing to chance.  Even better the instructional materials include an assessment of all the skills in subtraction computation in order, so you can test the knowledge of the student(s) before beginning instruction to see where to start. You can use this assessment to find very specific “holes” in student skills and then have the exact problems and explanation to fill that hole.

Note that the number for each skill gives the grade level as well as indicating the teaching sequence.  Skill 3b is a 3rd grade skill and after skill 3g is learned the next in the sequence, skill 4a is best taught in fourth grade.  Minor changes have been made, but for the most part, 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) Subtract from 2 digits; no renaming.

(2a) Subtract from 2digits; renaming required.

(2b) Subtract from 3 digits; borrow from 10s.

(3a) Subtract from 3 digits; borrow from 100s.

(3b) Subtract from 3 digits; borrow either place.

(3c) Subtract tens minus one facts.

(3d) Subtract from 3 digits; zero in 10s; borrow 10s or 100s.

(3e) Read and write thousands numbers, use commas.

(3f) Subtract from 4 digits; borrow from 1000s.

(3g) Subtract from 4 digits; borrow once or more.

(4a) Subtract from 4 digits; zero in 10s or 100s column

(4b) Subtract from 4 digits; zero in 10s column, 1 in 100s.

(4c) Subtract hundreds minus one facts.

(4d) Subtract from 4 digits; zero in 10s and 100s column.

(4e) Subtract 1, 2, or 3 digits from 1,000.

(4f) Subtract 5 and 6 digits with borrowing.

(5a) Subtract thousands minus one facts.

(5b) Subtract from a number with four zeroes.

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.  My favorite part is the rule students are taught for when to borrow (often confusing for students): Bigger bottom borrows.  Simple, easy-to-remember and consistently correct.  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.

Learning multiplication computation–NEW program in Rocket Math

Posted on by Dr. Don

After becoming fluent with multiplication facts the best way for students to retain the knowledge of those facts is by doing multiplication computation.  If students have not been taught multiplication computation, this program breaks it down into small, easy-to-learn steps that are numbered in a teaching sequence that leaves nothing to chance.  Even better the instructional materials include an assessment of all the skills in multiplication computation in order, so you can test the knowledge of the student(s) before beginning instruction to see where to start.

Note that the number for each skill gives the grade level as well as indicating the teaching sequence.  Skill 3b is a 3rd grade skill and after skill 3e is learned the next in the sequence is skill 4a.  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.

 

 

(3b) Multiplying 1-digit times 2-digit; no renaming

(3c) Multiplying 1-digit times 2-digit; carrying

(3d) Multiplying 1-digit times 2-digit, written horizontally.

(3e) Reading and writing thousands numbers, using commas.

(4a) Multiplying 1-digit times 3-digit

(4b) Multiplying 1-digit times 3-digit; zero in tens column

(4c) Multiplying 1 digit times 3 digit, written horizontally

(4d) Multiplying 2-digits times 2-digits.

(4e) Multiplying 2-digits times 3-digits.

(5a) Multiplying 3-digits times 3-digits.

(5b) Multiplying 3-digits times 3-digits; zero in tens column of multiplier.

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.

You have to require your students to model

Posted on by Dr. Don

Have them model the correction procedure rather than the latest fashions.

You can’t just tell your students the three steps of the Rocket Math correction procedure.  That’s not enough to be sure they know it.  The best way to determine if the students know the procedure is to require them to model it.

Do this, not just when you start Rocket Math, but any time you see that students are NOT doing the correction procedure the right way.  If they start to slip or zone out, the best thing to do is stop them from doing Rocket Math and spend a few days requiring them to model how to correct your errors, one at a time, while everyone listens.   Do it for ten minutes each day (during Rocket Math time) for several days–at least until you have had every student get a chance to “be your checker.”

Require them to model the correction procedures while you role play being a student making errors.

You have to role play being a student and you have to make the ALL the errors which they have to learn how to correct.  You have the worksheet and your students have the answer key in front of them.  Choose one at a time to be your “checker.”

First, ask that student WHEN should they should correct you.  They should say (in any order),

When you make an error. 

When you hesitate. 

When you say the problem wrong. 

When you don’t say the whole problem and the answer. 

Second, ask that student HOW they should correct you.  They should say (in order)

1.  Stop. Interrupt the student and say the correct problem and the answer.

2. Repeat.  Have the student repeat the correct problem and answer three times. 

3. Back up.  Have the student back up three problems and begin again.  

Third, begin practicing as if you were a student and then make errors.  Then require the student you’ve selected to be your checker to model the three-step correction procedure.   They should interrupt you and say the whole problem and the answer, ask you to say it three times, and then after you’ve repeated it three times, they should tell you to back up three problems and begin again.  You’ll end up counting together and coming to agreement about where to start and then beginning again.  But remember, they have to know not just HOW to correct, but also WHEN to correct.

Fourth, be sure to make all four kinds of errors to see if your “checker” recognizes all of them.  Try reading just the answers and see if your checker follows the correction procedure.  Definitely do a two second hesitation and if they don’t jump in to correct you, prompt them to do so.  Read the problem wrong as well as say the wrong answer.  Prompt the correction procedure if the student doesn’t do it the right way or at the right time.  If you have to prompt a student then they aren’t ready yet.  Keep going around the class, calling on each of your students to be your checker, and make sure they do it correctly and prompt them if they don’t.  Go back and call on any students who needed prompting and see if they can do it without prompting now. Keep making them model the correction procedure until everyone can do it the right way WITHOUT PROMPTING.

**The correction poster (pictured above) is available in the Rocket Math store under Organization and Training materials.  Item #2014 Corrections poster $18