## When to use the Learning Computation Learning Tracks

Once your student has mastered the math facts (reached Level Z) in one of the four arithmetic operations, the Rocket Math Learning Computation worksheet Learning Track takes this student seamlessly all the way to the top of that operation’s ladder (at the top is the highest skill in that operation).
I recommend you start using the Learning Addition Computation track as soon as the student has mastered the Addition facts, and while the student continues learning the facts in the other operations. When the student masters the facts in another operation, start the Learning Computation track for that operation. And so on.

## What’s in the Learning Computation worksheets?

The four Learning Computation tracks are divided into “skills.” Each skill in each step of the ladder, in the natural order in which one is to learn them. Dr. Don has created five worksheets for each skill in each Learning Computation track.
For each skill in each operation, Dr. Don has prepared the following:
1… The most detailed and helpful and concise instructions for that particular skill, for the teacher/parent to learn how to teach it.

I think the four LC tracks are amazingly valuable because they help learn the different skills…
1… thoroughly because there are plenty of problems to practice specifically the new skill
2… seamlessly because the jump from one skill to the next is almost imperceptible, so it is an easy jump to take
2… A set of five numbered worksheets. The top half in each Learning Computation sheet has problems with new skill learned in that particular five-sheet step. The problems in the bottom half of the worksheet are a review of the immediately prior skills.

## How to use the Learning Computation (LC) Worksheets

How does one use it? Easy. We simply started with skill 1 sheet 1 and then follow onto sheets 2, 3,4, and 5. Then, you move on to skill 2 sheet 1, etc. If, by the time your student is in sheet 5 of a given skill, you think they have not mastered it, then you go back a few sheets or even to sheet 1 in that skill.
The teacher’s script tell you exactly how to teach the skill–it asks the student questions about each step in the process, so they learn how to think about what they are doing.  The script has sections where it reduces the amount of prompting you provide, until by the end of the five sheets the student is totally doing it on his own or her own.
There are placement tests for each operation which gives you a chance to see which skills are already mastered and where he or she begins to make errors.  The placement tests would allow you to skip some of the skills your student already knows, and begin where he or she has difficulty.  But it isn’t required.  We were happy to just go in order without using the placement test.

## Doing Learning Computation in several operations

When our student was doing Learning Computation (LC) in three operations (addition, subtraction and multiplication, and was still learning division facts), we would do all three LC tracks each school day, but only the left or the right half of the sheet in question. So he would do the left half of addition, the left half of subtraction, the left half of multiplication. That way he was not doing too much each day, while still using the recently learned facts and learning the skill at hand.

## Learning Computation makes it a painless process

At the time of this writing, we have completed the Addition and Multiplication LC tracks. LC tracks Subtraction and Division still ongoing (subtraction because it is by far the track with largest number of different skills; division because he started it not too long ago). For our student and for us this has been and still is a painless process. We like very much that there is plenty of practice of the new skill in each set of five sheets, so that he is most of the time ready to move to the next skill by the time he finishes the fifth sheet.
For us, working on learning computation for several operations at the same time has been a great way for our student to refresh and use the math facts he worked hard to master.

Here are the four Learning Computation Learning Tracks in the Rocket Math Worksheet Program.

## Trophy for completing all 16 Learning Tracks

Dr. Don will send this trophy and a personalized certificate to any student who completes ALL 16 LEARNING TRACKS.  The first student in the world to earn this certificate and trophy for completing all 16 learning tracks in the Rocket Math Online Game was Addison H. of Whitehall, Wisconsin.

## Export their completed Learning Track Summary.

To see if any of your students qualify, export the Learning Track Summary.  A student who has completed all 16 Learning tracks will show their username listed with all 16 Learning Tracks completed all the way to Z.

A qualifying record would look like this, showing all 16 learning tracks and all with a fully completed level of Z.

Please note, this includes the Addition and Subtraction Learning Tracks 1 through 6, so you may have older students who will have to go back and finish those learning tracks.  Encourage them to do so–it’s good practice for them and will help them doing computation later in life.

## First time through only.

The offer of the trophy and certificate applies only to the first time through the Learning Tracks.  After becoming fluent, students can zip through the Learning Tracks much more easily than when they are first learning the facts.  The second time through students should often earn Fluency promotion allowing them to skip through a Learning Track in a few minutes.

Teachers, please send an email from your school account address to Angela@rocketmath.com.  Include your name or the name of the teacher who has worked with the student along with the student’s username and their actual first and last name, their grade level, and of course, the school mailing address so we can mail it to you.

Use this link to email it to Angela@rocketmath.com. When she confirms the data in your export Learning Track Summary, she will mail the certificate and trophy to you.

## Why teach Add to 20 facts?

The Common Core suggests that students be able to compute mentally facts  such as 11 + 7, 4 + 13, and 16 + 3.  These obviously build on the basic single digit facts such as 1 + 7, 4 + 3, and 6 + 3. Students should find these fairly easy to master but they still need some practice to commit them to memory.

LOOK OUT! Because all the answers are two digits, the number of problems students can be expected to answer will go down!

You must give the special Add to 20 Writing Speed Test to set new lower goals for your students.  Below you can see the sequence of facts that will be learned in the Add to 20 Learning Track.  Otherwise, this Learning Track is exactly the same as the basic Addition Rocket Math program and uses the same forms–that can be found in the forms and information drawer.

## Why teach Multiplication 10s, 11s, 12s facts?

This teaches  the 10s, 11s, and 12s multiplication facts, e.g., 10 x 7, 11 x 4, 12 x 6.  This Learning Track is optional.  Can be used by those students who have mastered the 0 through 9s Rocket Math multiplication facts.  Especially helpful for students who complete the 0s through 9s quickly and need something else to work on during “Rocket Math” time.  These facts are not critical to be able to do multi-step multiplication, but they are useful to know by memory.  The tens and elevens mostly follow a simple rule and aren’t hard to memorize.  Because there are 12 inches in a foot, it is helpful to know multiples of twelve, especially when measuring.  Finally, this is an excellent review because it includes cumulative review of the 0-9s facts while gradually teaching the 10s, 11s, and 12s facts.

## How does the Learning Track work?

This Learning Track includes the same Rocket Math process, worksheets, and routines. The sequence of facts learned in Multiplication 10s, 11s, and 12s can be seen above.

## What do students learn?

Students learn a systematic way of finding factor pairs, which results in being able to memorize the factor pairs of common numbers.

What are the factor pairs of 24? Answer: 1 and 24, 2 and 12, 3 and 8, 4 and 6. This is what students learn by memory.

By following our systematic “How to Factor” procedure, students are certain to find and remember all the factor pairs of common numbers.

Finding the greatest common factor and simplifying fractions will be a breeze after students learn this easy method and practice finding all the factors of these common numbers. Students learn all the factor pairs for these numbers in this sequence: 12, 36, 24, 48, 18, 32, 16, 64, 10, 40, 20, 72, 8, 25, 50, 6, 21, 30, 60, 15, 45, and 100.

## Video Lesson on “How to Factor” for students

Click here to see the critical “How to Factor” online video lesson from Dr. Don.

Or paste this into your browser so students can watch the lesson:  https://www.educreations.com/lesson/view/how-to-find-all-the-factors-of-a-number/46790401/?ref=link

## How students use this Learning Track

Students practice with a partner, take a daily one-minute timing, fill in a Rocket Chart, just like regular Rocket Math. There are also special directions for the things that are different in the Factors Learning Track.

Be sure to give the special Writing Speed Test for Factors. It’s found in the virtual filing cabinet drawer. It gives the student special goals for writing factor pairs.

## Mixed Integers combines Adding Integers and Subtracting Integers

If this mixed set goes too fast or is confusing for your students, an alternative is to start students with the two Learning Tracks that teach addition and subtraction separately.  The four addition processes are taught separately in the Learning to Add Integers Learning Track.   The four subtraction processes are taught separately in the Learning to Subtract Integers Learning Track.  If students have done those two Learning Tracks first, this will be a review and will be easier.

## Mixed Integers teaches eight processes and two rules.

Mixed Integers displays problems on a vertical number line and then teaches students two rules about how to solve problems that add or subtract positive and negative numbers.
Rule 1:  When you add a positive number OR subtract a negative number, go UP.
Rule 2:  When you subtract a positive number OR add a negative number, go DOWN.

Students learn how these rules play out when starting with a positive number and a negative number, gradually learning these two variations of all four types of problems.  They learn to solve a problem type using the number line and then to recognize the pattern of each problem type by working several examples of each type.  This practice gives them a chance to build fluency with each problem type as they work with their partner on the top half of the page.  You will probably not be surprised that there is a one-minute test on each set.  The goals are slightly different than before.  Students are to be 100% accurate and to meet or beat their goal from the special writing speed test for mixed integers.

## Video lessons teach the 8 processes.

There are 8 types of mixed integers problems (see below), between positive and negative numbers and the two operations. 8 online lessons teach students how each type of problem is solved and why it is correct.  (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

## How does this Learning Track teach?

Learning to Subtract Integers displays problems on a vertical number line and then teaches students two rules about how to solve problems in which you subtract positive and negative numbers.

Rule 1:  When you subtract a positive number, go DOWN.
Rule 2:  When you subtract a negative number, go UP.

Doing problems on the vertical number line is more intuitively appealing because UP is more and DOWN is always less.  This makes crossing zero a little easier to comprehend.

### Total of four problem types to learn.

Students learn how these two rules play out with two types of problems: when starting with a positive number and when starting with a negative number. Students gradually learn all four types of problems.  On each worksheet they see how to solve each problem type using the number line working with their partner.  Then students learn to recognize the pattern of each problem type by orally answering several examples of each type with their partner (going around the outside of the page).  You will probably not be surprised that there is a one-minute test on each set.   Students are to be 100% accurate and to meet or beat their goal from the special writing speed test for Learning to Subtract integers (the fastest goal is only 28 problems in a minute).

## Online Video lessons can teach students the process.

Here are links to the 4 online lessons teach students how each type of problem is solved and why it is correct. These are available in the virtual filing cabinet as well.

(1) Subtract Integers Set A Positive subtract a positive

(2) Subtract Integers Set B Positive subtract a negative

(3) Subtract Integers Set G Negative subtract a negative

(4) Subtract Integers Set L Negative subtract a positive

## What is Skip Counting?

Not counting while skipping!  Learning to skip count by fours is to learn this sequence by memory: “Four, 8, 12, 16, 20, 24, 28, 32, 36, 40.” Skip counting is also known as learning the “count-by” series.

## Why teach skip counting?

Skip counting is the best way for students to prepare for multiplication. It teaches the concept of successive addition which is the root of multiplication.  In addition, skip counting helps prepare the ground for memorizing the multiplication facts.  Students who have learned to skip count find the chore of memorizing multiplication facts much easier. This Learning Track is excellent for second or third grade students after learning addition and subtraction facts and before learning Multiplication facts. Skip counting is not something older students past fourth grade really need to do, and of course, it’s no longer useful once multiplication facts have been committed to memory.

## Each series is broken into easy-to-learn parts

Students learn part of each sequence on a page, then the next page they learn the rest. For example: in Set O students learn to count by 3s to 12, (3, 6, 9, 12) then in Set P they learn to count by 3s to 21 (3, 6, 9, 12, 15, 18, 21), and then in Set Q they learn to count by 3s to 30 (3, 6, 9, 12, 15, 18, 21, 24, 27, 30).

## How does Skip Counting teach?

As in most Worksheet program Learning Tracks, students practice with a partner who has the answers. Because of the way the rockets go around the page (see above), students and their checkers will have to pick up the pages and turn them as they are working. You’ll be able to see if they are really engaged and they will have fun turning the page around. The test in the center has them write the count-by series they have learned for one-minute and they need to meet or beat their best–just like the rest of Rocket Math. Here is the sequence students will learn in this order: 2s, 5s, 10s, 9s, 4s, 25s (so they can count quarters), 3s, 8s, 7s, and 6s. Probably our most fun Learning Track.

## What does this Learning Track teach?

Learning to Add Integers teaches four types of problems to solve.  It displays problems on a vertical number line and then teaches students two rules about how to solve problems that add positive and negative numbers.
Rule 1:  When you add a positive number, go UP.
Rule 2:  When you add a negative number, go DOWN.

Doing problems on the vertical number line is more intuitively appealing because UP is more and DOWN is always less.  This makes crossing zero a little easier to comprehend.

Students learn how these two rules play out with two types of problems: when starting with a positive number and when starting with a negative number. Students gradually learn all four types of problems.  On each worksheet they see how to solve each problem type using the number line working with their partner.  Then students learn to recognize the pattern of each problem type by orally answering several examples of each type with their partner (going around the outside of the page).  You will probably not be surprised that there is a one-minute test on each set.   Students are to be 100% accurate and to meet or beat their goal from the special writing speed test for Learning to Add integers (the fastest goal is only 28 problems in a minute).

## Video Lessons for students to learn the process.

4 online lessons teach students how each type of problem is solved and why it is correct.

## Add and Subtract Fact Families are a different way to learn facts.

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. This program is Part 2 of Fact Families, coming after Fact Families 1 to 10. You can see above the 18 examples of fact families taught in this program starting with Set A; 11-2, 11-9, 9+2, & 2+9.  The sheet above shows the sequence of learning facts in the new Rocket Math  program Add-Subtract Fact Families from 11 to 18.  Each set that students learn from A to R 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.

## Fact Families from 11 to 18 is part two and fit for second grade.

These facts come after the Add and Subtract Fact Families 10, which should be learned in first grade, so these are best for second grade.  The 25 fact families in 1s through 10s facts are just enough for one Rocket Math program.  It is a good and sufficient accomplishment for first grade.  With the 11 to 18 part for second grade there will be a lot of review.  In fact sets S through Z are all review. 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.

We  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 us feedback when you use this program, Add-Subtract Fact Families 11 to 18,  letting us know how it goes for the students.