Fraction & Decimal Equivalents Learning Track

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Fractional & Decimal Equivalents

This learning track gives students practice in identifying four kinds of equivalents.  All the equivalents practiced in this learning track are listed in the sequence shown at the top of the page.  In the virtual filing cabinet you can also print out the sequence. Note that this is Learning Track 16 in the Online Tutor.

Decimals that are equivalent to common fractions

The first type of equivalents students learn are decimal numbers to a fraction.  An example is 0.667 is equivalent to the fraction 2/3.  Decimals such as 0.4 = 2/5 or 0.25 = 1/4 or 0.125 = 1/8 are practiced.  Twenty-five of these equivalents are learned.  These are the most important items and are the equivalents that get the most practice.

Fractions in decimal form (tenths and hundredths)

A second kind of equivalent is that of a fraction in decimal form, such as 66.7/100 (which is equivalent to the fraction 2/3).  Another example is 4/10 which is equivalent to 2/5.

Fractions equivalent to division problems and vice versa

The other two kinds of equivalents show the interchangeability of division problems and fractions.  The fraction 2/3 is equivalent to dividing 3 into 2.  Conversely, dividing 3 into 2 is equivalent to the fraction 2/3.   These are introduced, but because they follow a rule, these are not tested as thoroughly as the decimals equivalent to fractions.

 

 

 

Rounding up to Millions Learning Track

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Rounding up to Millions

This learning track gives students practice in rounding to the nearest ten thousand, nearest hundred thousand and nearest million.  Students practice with numbers with varying numbers of digits, starting with 3-digit numbers and going up to 5-digit numbers.  The sequence of the kinds of numbers students learn to round is shown above.

Each worksheet includes four examples of rounding.

We give four examples of rounding at the top of each worksheet so that students can see how to round each type of number.  Then students work with their partner, who has the answer key, to round the numbers around the outside. The student says the “answer” which is the rounded number.  The partner corrects errors by saying the number and what it rounds to aloud, (e.g., “8,621 rounds up to 9,000”) and follows the same correction procedure: Ask the student to repeat the correct information three times, then back up three problems.

1-minute Daily test requires writing only 3 numbers

The Daily Tests do not require the student to write out the complete number.  Instead, they only have to write three digits of the rounded number.  This allow students to answer more questions in the one-minute test.

 

 

Rounding up to Thousands Learning Track

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Rounding up to Thousands

This learning track gives students practice in rounding to the nearest ten, nearest hundred and nearest thousand.  Students practice with numbers with varying numbers of digits, starting with 3-digit numbers and going up to 5-digit numbers.  The sequence of the kinds of numbers students learn to round is shown above.

Each worksheet includes four examples of rounding.

We give examples on each worksheet so that students can see how to round each type of number.  Then students work with their partner, who has the answer key, to round the numbers around the outside. The student says the “answer” which is the rounded number.  The partner corrects errors by saying the number and what it rounds to aloud, (e.g., “8,621 rounds up to 9,000”) and follows the same correction procedure: Ask the student to repeat the correct information three times, then back up three problems.

1-minute Daily test requires writing only 3 numbers

The Daily Tests do not require the student to write out the complete number.  Instead, they only have to write three digits of the rounded number.  This allow students to answer more questions in the one-minute test.

 

 

Learning Computation with Rocket Math Worksheets: A customer review

We strongly recommend the Rocket Math Learning Computation four tracks for any homeschool. We hope you find this review helpful.

JL Marcos family, Jacksonville Beach, Florida

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.

Award Medallion for completing all 16 Learning Tracks

Rocket Math will send this medallion* and a personalized certificate to any elementary student who completes ALL 16 LEARNING TRACKS.  The first student in the country to earn this certificate 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 elementary students qualify, export the Learning Track Summary. Here’s how to do this.  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. 

The award is earned only on the first time an elementary student passes through the Learning Tracks.

The offer of the medallion and certificate applies only to the first time an elementary student passes 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. 

Contact us to get the medallion and certificate.

Elementary 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 medallion to you.

*We’ll pay for shipping the medallion within the United States.  If you’re outside the US, we will ask you to cover shipping costs. 

Post this pdf in your room to motivate your students

BONUS CHALLENGE–CAN YOU DO ROCKET MATH on the FAST SETTING?

Add to 20 (e.g., 13+6, 4+11, 15+5) Learning Track

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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.

Multiplication 10s, 11s, 12s Learning Track

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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.

Factors (finding all the factor pairs) Learning Track

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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.

Read more about this method on this blog or watch the video below.

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 (adding and subtracting positive and negative numbers) Learning Track

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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

 

Learning to Subtract Integers (positive and negative numbers) Learning Track

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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