When students begin to pass levels in Rocket Math, and color in the Rocket Chart in their folders, they naturally are proud of their accomplishments. Students want to tell me what level they are “on” when I visit classrooms. Unhealthy competition may develop among students sometimes. Some students begin to feel really bad about their slower progress, and students in the lead act arrogantly or disrespectfully. The Rocket Math Wall Chart is designed to curb that competition.
The Wall Chart puts all the students on the same team.
Over 700 star stickers come with the Wall Chart. Each time a student passes a level the teacher awards them with a star sticker, which they take up to the Wall Chart and put into one of the squares in the chart. Students fill the chart from the bottom up. The teacher sets a goal in a few weeks, which date is marked on the goal arrow, and the goal arrow is placed a couple of rows up from where the students are now. (You can just see that in the picture above.)
Students develop pride in their whole class.
If the students fill in the squares up to the arrow–before the date specified on the arrow–they earn a group reward such as extra recess time, or music during math, or a congratulatory note home, or a popcorn party, etc. In this way, each time a student passes a level they are putting up a score for the whole team. It is good for everyone. The teacher is able to praise the class for their hard work and accomplishments, and the whole class is able to feel good about their collective effort.
The Wall Chart shows visitors (like principals) how well the class is doing.
Passers-by as well as interested administrators can praise the class as a whole for their successes with Rocket Math. In many schools, classes post their completed Rocket Chart on their door with all 725 stickers in place! The Rocket Math Wall Chart becomes a focus of pride and recognition for the whole class. The price for the Rocket Math Wall Chart (#2005) of $20 includes directions, plenty of star stickers, four goal arrows, and the chart itself. They are cheaper by the dozen, $155 for all twelve.
You want your middle-grade students to complete the pre-algebra math topics so they are ready to begin to study algebra in 8th or 9th grade. A disheartening number of middle-grade students have not memorized basic multiplication facts (times tables). Students must know multiplication facts to follow, absorb, and implement pre-algebra topics. How to teach multiplication facts to struggling students? How can a teacher help their struggling students learn multiplication facts when a lot of their students do not need to do that work?
Rocket Math Online Game includes learning tracks for pre-algebra skills as well as basic multiplication and division facts. Within the Rocket Math Online Game, teachers assign students the learning tracks that they most need.
Math Strategies for Struggling Students
Students who do not know their multiplication facts are constantly distracted from learning math strategies by having to stop and “figure out” basic facts. Every time they are asked to provide the answer to a multiplication fact, they have to turn their attention to working it out or looking it up. By the time they have gone through their process, they have lost the thread of the strategy they are supposed to be learning. The most important thing a math teacher can do for struggling math students is to help them bring math facts to automaticity. Then answering math fact questions no longer interferes with learning multi-step strategies for solving math problems.
Why Multiplication facts are Important to Learn Before Middle School Math
Many pre-algebra math topics assume students have a ready knowledge of multiplication facts to even understand. When I was a middle-grade teacher, my remedial students were unable to follow or understand topics such as Finding factor pairs, reducing fractions, equivalent fractions, converting fractions, unlike fractions, and so on. I realized that it was because they did not know basic multiplication facts. When I reduced 8/24 to ⅓ it was like magic because they did not quickly recognize the multiplication facts involved. They didn’t understand the concepts we were trying to learn because they did not see the relationships they were supposed to know. When I asked them to think of the factor pairs of 36 they were unable to find them all, no matter how much time I gave them. While students can do multi-digit multiplication problems using a times table chart, it does them no good in pre-algebra topics because it takes too long, even if they know what to look up. Now let’s look at how to teach multiplication to struggling students using Rocket Math Worksheets or Rocket Math Online Game.
How to Teach Multiplication to Struggling Students Using Rocket Math
Students who have not yet mastered multiplication facts are going to require a very effective teaching methodology to learn them. The haphazard, leave-it-up-to-the-student methods have already failed them. By now, these students lack confidence in their ability to learn the facts, so you need a sure-fire system.
Rocket Math is just such a system. Both the Worksheet Program and the Online Game systematically introduce students to the facts in a careful sequence that they can do. The Worksheet Program and Online Game ask students to memorize only two facts and their reverses at a time.
Students demonstrate mastery of those facts by answering them without hesitation. Then Rocket Math will add two more facts and their reverses. Small steps at a time, systematically the students can memorize the facts and answer them instantly from memory. If students practice every day, within a few weeks you’ll see a dramatic improvement in their recall of multiplication facts.
But what about the students who already know their multiplication facts? Rocket Math has something for them as well.
Rocket Math Programs for Advanced Students
Teachers can assign Rocket Math as a 10-minute warm-up or cool down for all their students whether they are behind or advanced. Rocket Math has several pre-algebra topics for those students who already know their multiplication facts. Each of these topics will help them do pre-algebra processes more fluently and to quickly recognize relationships that they have memorized.
When students initially learn about fractions they are often only shown proper fractions. As a result, they have a limited understanding of fractions and can be confused by improper fractions or mixed numbers. The Rocket Math programs (both Worksheet and Online) prevent this problem. From the start, we teach students using examples of both proper and improper fractions as well as whole numbers and mixed numbers. Students learn to identify over 90 different fractions quickly and easily by getting lots of practice. Their understanding of fractions will deepen and become more flexible as they learn to recognize many examples of fractions.
Students will memorize the most common equivalent fractions with this Rocket Math Learning Track. They will also learn to identify a number of fractions, such as 2/9, that do not “reduce” or for which there are no equivalent fractions in lower terms. Students also learn to recognize a fraction equal to 1 whole in its various forms. When students don’t instantly know the answer they are told the equivalent fraction and given practice on it. The computer gives help in the Online Game. Their partner gives that help in the Worksheet Program. By the end of the program, students will learn over 90 equivalent fractions. This gives students an excellent start on being able to manipulate fractions quickly and easily.
Students are required to “find the factors” when dealing with unlike fractions and reducing fractions. Rocket Math Worksheet and Online Game teach students how to find factor pairs. Students learn how to find all the factor pairs and what they all are for many common numbers. They also learn to identify prime numbers and their characteristic of having only one and themselves as factors. Students learn the factor pairs in order and know the “last” factor pair when they see it. When the game asks “What’s next?” students can provide the next pair of factors or click the checkmark to indicate there are no more factors. When students go through this Learning Track they will no longer hesitate when asked for the factors of common numbers.
Learning Track 16: Fraction & Decimal Equivalents
Common fraction and decimal equivalents should not require a laborious process to “figure out.” Students should just know these, so this Learning Track in the Online Game allows them to memorize a bunch of common decimal and fraction equivalents. Having a facility with a lot of fraction and decimal equivalents means faster computation as well as a way to check their process when manipulating fractions and decimals. Students also learn another essential pre-algebra skill that often confuses them. They learn to correctly and fluently translate a fraction into a division problem and vice-versa.
Basic, Optional, and Alternative—there are a lot of different Rocket Math programs. But which program should you use first? And in what order should you teach fast math facts? Well, it all depends on the grade you teach and the fast math facts your students have already memorized.
An overview of Rocket Math’s fast math fact programs
Rocket Math’s basic program includes Addition, Subtraction, Multiplication, and Division (1s-9s). The basic program must be mastered by all students.
The Alternative Program: Fact Families
There is another way to learn facts, which is called Fact Family math. Instead of learning all Addition facts, students can learn Addition and Subtraction facts at the same time. A fact family consists of four related facts, for example: 3+2 = 5, 2 + 3 = 5, 5 – 3 = 2, 5 – 2 = 3. As an alternative to using the Basic Program, students can learn fact families up to 10 in first grade. Then students can move on to the upper fact families 11 to 18 in second grade. There is no clear evidence that this way is better or the separate operations way is better. That’s why we offer both options.
The rest of the fast math facts programs like Rocket Writing for Numerals or Skip Counting are optional. You should only offer these programs to students once they have memorized the fast math facts through the Basic Program or the Alternative Program.
The only exception would be in a school where Kindergarten students did not get a chance to learn how to quickly and easily write numerals. In that case, you might take the first two months of the first grade year to run students through Rocket Writing for Numerals before beginning Addition (1s-9s).
Let’s take a closer look at how to implement each program in different grade levels.
First grade math facts: Learn Addition
Rocket Math fast math facts programs for first graders include:
The Basic Program
The Alternative Program
Fact Families (1-10) Add & Subtract
Rocket Writing for Numerals
Add to 20
If first grade students are taking all year to get through sets A-Z in Addition in the Basic Program, they need some extra help. You should intervene to help students who take more than a week to pass a level. Often they need to practice better or practice with a better partner. Some may need to practice a second time during the day or at home in the evening. First grade students who finish the 1s-9s can move on to the Add to 20 Optional Program for the remainder of the year.
Likewise, if you choose to teach Fact Families (1-10) Add & Subtract from the Alternative Program instead of using the Basic Program, your students can use the Optional Programs for supplemental learning purposes.
Second grade math facts: Learn Addition and Subtraction
Rocket Math fast math facts programs for second graders include:
The Basic Program
The Alternative Program
Fact Families (1-10) Add & Subtract
Fact Families Part Two (11-18) Add & Subtract
Subtract from 20
Second grade students must have completed Addition before starting on Subtraction (1s-9s). They can also test out of Addition through the Placement Probes. Second graders who cannot test out of Addition in first grade or didn’t complete it in first grade must focus on Addition. Only after getting through Set Z of Addition should they move into Subtraction.
You can substitute the Basic Program’s (1s-9s) Addition and (1s-9s) Subtraction for the Alternative Program’s Fact Families (1-10) Add & Subtract and Fact Families Part Two (11-18) Add & Subtract.
Second grade students who complete Addition and Subtraction 1s-9s (or the Alternative Program) can move on to Subtract from 20. Students who finish Subtract from 20 can do Skip Counting, which does a great job of preparing students to learn Multiplication facts.
Third grade math facts: Learn Multiplication
There aren’t any Alternative Programs available for third graders from Rocket Math. There are only Basic and Optional Programs. These include:
The Basic Program
(1s-9s) Multiplication (priority)
10s, 11s, 12s Multiplication
In third grade, Multiplication has priority—even if students have not mastered Addition and Subtraction. Multiplication facts are so integral to the rest of higher math that students are even more crippled without Multiplication facts than they are having to count Addition and Subtraction problems on their fingers. So do Multiplication first. Then, if there’s time, students who need to do so can go back and master Addition and Subtraction. Once all three of these basic operations are under their belts, students can go on to 10s, 11s, 12s in Multiplication (one of the Optional Programs). If students successfully progress through each program and there is enough time left in the school year, introduce the Factors program next.
Fourth grade math facts: Learn Multiplication and Division
Like the programs for third graders, there aren’t any Alternative Programs available for fourth graders. There are only Basic and Optional Programs, which include:
The Basic Program
(1s-9s) Multiplication (priority)
(1s-9s) Division (second priority)
10s, 11s, 12s Multiplication
In fourth grade, students need to have completed Multiplication before going on to Division. If they complete Division, they can go on to 10s, 11s, 12s Division, followed by Factors, and then equivalent fractions (shown in the fifth grade section below).
Fifth grade math facts: Learn all basic operations first, then they can branch out
By fifth grade, students should have completed all four basic operations (1s-9s) within the Basic Program (or the Alternative Program for grades one and two). If students have not completed these basics (and cannot test out of them with the Placement Probes) then the sequence they should follow is Multiplication, followed by Division, then go back and complete Addition followed by Subtraction. The same recommendations hold for students in any grade after fifth.
Once students have mastered the basics (1s-9s add, subtract, multiply, divide), the supplemental pre-algebra programs are recommended. These will help more than learning the 10s, 11s, 12s facts. I would recommend this order:
Here’s information (that may not be apparent) about the next step–after registering for a free account for the Rocket Math Online Game. The next step is to to try out the game with some students by signing up for our No risk 30 day trial.
Your credit card will not be charged until the end of your 30 day trial, so if you cancel before then you do not pay a thing. You can order from the “My Profile” page of your account with a credit card to order subscriptions. It looks like this picture.
No gotcha here–See how the auto-renew is turned off by default?
Leave the renewal period set to monthly, and leave auto renew set to OFF in your profile.
Your subscription will simply end after 30 days.
No matter how many subscriptions you order, your credit card won’t be charged until you login and renew. So you can try the game for free to see if it’s worth paying for with no risk of being charged for it.
Either in PayPal or with a PO we will give you 13 months, and if you tell us you don’t want it during the first month, we’ll cancel your subscription and cancel the invoice. With PayPal we’ll give you a full refund if you don’t want to keep it.
If you ask, I can also manually give you a 30 day free trial–without you having to enter a payment method. Then we can send an invoice if you wish to continue. Just contact [email protected], with the number of subscriptions you would like to use during your free trial.
Learning to Add Integers 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.
Click to see online lesson. 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).
Students can watch 4 online lessons which teach how each type of problem is solved and why it is correct.
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.
Dr Don has a white board type video lesson that explains this in 6 minutes.
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.
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.
Can I upgrade from basic to universal? Will I just pay the difference?
Dr. Don answers:
Yes, indeed. If you login to your account you can see a link to upgrade (pictured above). Yes you will pay the difference between your current subscription and the upgrade. Good decision to upgrade! Once you upgrade you will be able to get into the drawers of the Universal subscription. All of these are included:
Rocket Writing for Numerals,
Add to 20,
Fact families (+, -) 1-10s,
Subtract from 20,
10s, 11s and 12s (Multiplication and Division),
Integers (adding and subtracting positive and negative numbers, etc.
I also have completed and added to the Universal Subscription programs to teach computation. The instruction proceeds in small steps from the beginning skills in an operation up through the highest levels. Each skill taught has a suggested teaching script to make it easy for tutoring. So far Addition and Multiplication are done. Each one has a placement test, so you can see where to begin. Subtraction and Division are yet to be completed.
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.
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.
It sure does, if you’re seeing this happen in your class!
Most middle school math teachers confide to me that their classrooms are negatively impacted by the number of students who stop to count out facts on their fingers. Their issue was always what to do during facts practice with the other students who do know their facts. It has taken a couple of years but I have put together a package of pre-algebra skills that are worth middle school students’ time practicing which are available in the Universal Subscription. Because the routine of Rocket Math is the same whether the students are practicing basic multiplication facts or learning equivalent fractions you’ll be able to manage all these different levels during the same ten-minute session.
Teachers know it is imperative that finger-counting middle schoolers get practice learning their facts. Rocket Math is an excellent way to do that. They will develop fluency and automaticity with the basic facts in an operation in a semester and from then on your lessons will be much easier. Not only that, but a much higher proportion of the students will be finishing assignments. There is a “Placement Probe” that can identify students who know their facts in about one minute. The students who know the basic facts of multiplication and division can be placed into the pre-algebra practice programs.
FACTORS. Students probably ought to begin with the Factors program. What are the factors of 24? Answer: 1 and 24, 2 and 12, 3 and 8, 4 and 6. This is what students learn by memory from doing this program. Students practice with a partner, take a daily one minute timing, fill in a Rocket Chart, just like regularRocket Math. Students learn all the factors 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.
EQUIVALENT FRACTIONS. Students need to know that six-eighths is equivalent to three-fourths and that four-twelfths is equivalent to one-third. While they can calculate these, it is very helpful to know the most common equivalent fractions by memory. One of the most common problems students have in fractions is not “reducing their answers to simplest form.” Equivalent fractions will help students commit 100 common equivalent fractions to memory. Each set (A through Z) has four fractions which are displayed on a fraction number line. Students frequently learn fractions equivalent to one,such as ten-tenths, as well as fractions that can’t be reduced, for example three-fourths is equivalent to three-fourths. Using the fraction number line will help with student understanding of why those fractions are equivalent.
INTEGERS(Adding and subtracting positive and negative numbers). 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: Go up when you add a positive number OR subtract a negative number.
Rule 2: Go down when you subtract a positive number OR add a negative number.
Students gradually learn several variations of all four types of problems. They practice with the number line on each page and then have a chance to build fluency on the top half of the page as they work with their partner. 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 complete at least 80% of their rate at answering simple addition and subtraction problems.
Among these five programs there are good things for ALL middle school math students to learn, even the more advanced students. This will enable a math teacher to devote ten minutes a day to fact practice without holding anyone back. Everyone will have something meaningful to practice during that time. I think this could be a huge step forward for a lot of middle school MATH classrooms.