To prove whether students are making progress in learning math facts.
First of all, understand that the two-minute timings are NOT a teaching tool. They are an assessment tool only. Giving a two-minute timing of all the facts in an operation every week or two allows you to graph student performance. You graph student performance to see if it is improving. If the graph is going up, as in the picture above, then the student is learning. If the graph is flat, then the student is not really learning.
The individual graphs should be colored in by students allowing them to savor the evidence of their learning. The graphs should be shared with parents at conference time to prove that students are learning.
Progress monitoring with two-minute tests are a curriculum-free method of evaluating a curriculum. If you use the same tests you can compare two methods of learning facts to see which one causes faster growth. This makes for a valid research study.
This kind of progress monitoring over time is also used in IEPs. You can draw an aimline from the starting performance on the two-minute timing to the level you expect the student to achieve by the end of the year. (Note the writing speed test gave you goals for the two-minute timing which you could use for your end-of-year goal.) The aimline on the graph, when it crosses the ending date of each quarter, will provide quarterly objectives that will enable quarterly evaluation of progress–required for an IEP.
These two minute timings are a scientifically valid method of proving whether students are learning math facts, in the same way that tests of oral reading fluency prove whether students are learning to read. They can be used to prove to a principal or a curriculum director, for example, that Rocket Math is working and is worth the time, paper and money it requires.
Using a vertical number line can help provide certainty.
Adding and subtracting positive and negative numbers can be confusing for students. You can either start with a positive or a negative number and you can combine with a positive or a negative number. That makes for four types or patterns of problems. Then when you consider both addition and subtraction the total is 8 problem types. Rocket Math has three learning tracks to help students learn how to deal with integers. Mixed Integers includes all eight types, whereas Learning to Add Integers and Learning to Subtract Integers each just deal with four types. [Mixed Integers may be too hard for some or all of your students–meaning they can’t pass levels in 6 tries. In that case put them through the Learning to Add Integers and Learning to Subtract Integers first.]
Part 1: Using the vertical number line to solve integers problems
The first issue for students is just to be certain of the answer. A vertical number line, where “up” is more and “down” is less helps provide certainty.
I have posted a series of free lessons online (links below) that use a vertical number line and a consistent procedure to take the confusion out of the process. All eight types of problems can be solved with the same process on the vertical number line. Using the vertical number line there are two rules to learn. Rule 1: When you add a positive or subtract a negative you go up on the number line. Rule 2: When you subtract a positive or add a negative you go down on the number line.
So first thing to figure out is what you are being asked to do (add or subtract a positive or a negative) and then use the rule to tell you whether whether you’re going up or down. Next step in the procedure is to circle the starting point on the number line. Once you circle the starting point, you show how far you’re being asked to go. You simply make the right number of “bumps” going either up or down from where you start. That gives you the answer without any uncertainty. These online 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.
Part 2: Using the Rocket Math Integers learning track(s) to develop fluency in recognizing the type of problem
Here is a part of a page from the Mixed Integers learning track. The paired practice part of the program helps students learn to quickly and easily recognize each pattern. First students use the vertical number line to work a problem. In this example: -6 minus (-4). Then they have a set of problems with the same pattern (a negative subtracting a negative) which they should be able to orally answer without having to use the number line. Each worksheet includes all the types learned so far in the learning track.
As with all Rocket Math programs there is a 2 to 3 minute practice session (at this level I’d recommend 3 minutes), with a partner. Then the two switch roles. The practice is followed by a one-minute test. If the student can answer the problems in the test fluently (essentially without hesitations) the level is passed. As always, the students goals are individually determined by a Writing Speed Tests. If a given level is still difficult the student stays with that level a bit longer.
When a new pattern or type of problem is first introduced the one-minute 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 in a row, culminating in the fifth level where the problem types are mixed. This way the student develops fluency in recognizing the type of problem and how to derive the answer quickly. The Learning to Add Integers and Learning to Subtract Integers learning tracks take more time to learn the patterns, while Mixed Integers moves more quickly.
Don’t forget that Rocket Math has a money-back guarantee. So if this doesn’t work for you and your students we will refund your subscription price.
Many students find integers confusing. If you add a negative to a negative are you getting more or less??? Over the years different “rules” have been used to try to remember what should happen. Rules such as “two negatives make a plus” or “opposite signs subtract.” Whatever is used to try to remember, it interferes with a student’s ability to quickly and reliably get the answers without having to stop and puzzle it out.
I have posted a series of free lessons online (links below) that use a vertical number line to take some of the confusion out of the process. Turns out there are a total of eight types of problems but all of them can be solved with the same process on the vertical number line. Intuitively on a vertical number line, up is more and down is less.
Using the vertical number line there are two rules to learn. Rule 1: When you add a positive or subtract a negative you go up on the number line. Rule 2: When you subtract a positive or add a negative you go down on the number line.
So first thing to figure out is whether you’re going up or down. Once you do that you simply make “bumps” going either up or down from where you start. That gives you the answer without any uncertainty. These lessons are quick (about 2 minutes) and identify a pattern of whether the answer is like the sum or the difference between the numbers. Once students can recognize the pattern they can begin to answer fluently and without a struggle.
To help with the work of learning to quickly and easily recognize each pattern in Integers Rocket Math now includes a “Mixed Integers” program in our Universal Subscription. (Click here to get a 60-day trial subscription for $13 –rather than the standard $49 a year.) Students use the vertical number line to work a problem. In this example: -6 minus (-4). Then they have a set of problems with the same pattern they can orally answer without having to use the number line.
As with all Rocket Math programs there is a 3 minute practice session, with a partner. Then the two switch roles. Then the practice is followed by a one-minute test. If the student can answer the problems without hesitations the level is passed. If it is still difficult the student stays with that level a bit longer. When a new pattern is introduced the tests will have a whole row of problems that are the same pattern. When that level is passed the next test will have two types of problems in each row. The next level has 3 types, then 4 types in each row. Then the problem types are mixed. This way the student develops fluency in recognizing the type of problem and how to derive the answer quickly.
Rocket Math has a money-back satisfaction guarantee. If you try this and find it isn’t everything you hoped, in terms of helping your students become fluent with integers, I’ll gladly refund your money. I’m betting they’re going to love it.
If student progress slows you need to improve practice.
When students are seeing regular success in Rocket Math, when they see themselves progressing, 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. If they start to complain about doing Rocket Math, then something is amiss. You need to correct the implementation BEFORE that happens.
Students should pass a level in no more than 6 days. There’s a 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, when you don’t intervene to help that happen they get discouraged. Any student who is not passing in six days needs to either improve the quality of their practice or the amount of their practice–or possibly both.
Intervene to improve the QUALITY of practice.
- 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?
- 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
Intervene to increase the QUANTITY of practice.
Some students need two practice sessions each day, what football teams call “2-a-days!”
*** Motivation is composed of the incentive and the belief that it can be done.***
Rocket Math App received 4 Stars!
App Names: Rocket Math Add at Home, Add at School, Multiply at Home, and Multiply at School
App Link :
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.
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.
I have a white board type video lesson that explains this in 6 minutes. https://youtu.be/fDYMRfxtGIc
Bookmark this link so you can show it to your students.
How to find all the factors of numbers
Always begin with 1 and the number itself-those are the first two factors. You write 1 x the number. Then go on to 2. Write that under the 1. If the number you are finding factors for is an even number then 2 will be a factor. Think to yourself “2 times what equals the number we are factoring?” The answer will be the other factor.
However, if the number you are finding factors for is an odd number, then 2 will not be a factor and so you cross it out and go on to 3. Think to yourself “3 times what equals the number we are factoring?” There’s no easy rule for 3s like there is for 2s. But if you know the multiplication facts you will know if there is something. Then you go on to four—and so on.
The numbers on the left start at 1 and go up in value. The numbers on the right go down in value. You know you are done when you come to a number on the left that you already have on the right. Let’s try an example.
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.
Four steps to get back into your account with a new password
Step 1: Get to the login screen and click on “Reset Password.”
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.”