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Learning to Subtract Integers (positive and negative numbers)
Part of the Universal Subscription Plan
Four Problem Types to Learn
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.
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).
4 online lessons teach students how each type of problem is solved and why it is correct.
(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
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These are the basic single digit Multiplication facts 1s through 9s. Each of the 26 levels, A through Z, introduces two facts and their reverses. You can see in the picture above of Set C, I have outlined the new facts in red.Students practice orally with a partner, reading and answering the facts going around the outside of the sheet. The partner has the answer key. Then the two students switch roles. After practice everyone takes a one minute test on the facts in the box–which are only the facts learned up to this level. Each student has individual goals based on writing speed, but no one can pass a level if there are any errors. You must give the special Writing Speed Test to set individual goals for your students.
Students should be able to pass a level in a week, if they practice the right way. To the right you can see the sequence of facts that will be learned in the Multiplication 1s-9s program. The program uses the four forms–that can be found in the forms and information drawer.
The most succinct way to be introduced to this program is this 8 minute video.
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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 left the 25 examples of fact families taught in this program starting with 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.
Best fit for first grade. I separated out the 1s through 10s facts from the 11s-18s, because these 25 families are just enough for one Rocket Math program. It is 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. 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.
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Everything you need** to set up an exciting and engaging Game Center in which students compete against themselves to beat their best time completing the Race for the Stars Game boards. Students time their partner completing the game board and post the time on the included poster using the included pen. A sheet of 60 computer-ready Avery name labels is also included. When students beat their posted personal best they put up the new time and cover the old time with a star sticker (plenty are included). A place for best times for both the A-K game board and the L-Z game board. Directions are included.
Click here if you want to read the directions now.
**Except the stopwatch and the games. If you need a stopwatch order item #2112 for $49.
If you need a Race for the Stars Game you must purchase it separately (for $24) you can find it here. -
After becoming fluent with division facts the best way for students to retain the knowledge of those facts is by doing division computation. If students have not been taught division computation, this program breaks it down into small, easy-to-learn steps that are numbered in a teaching sequence that leaves nothing to chance.
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 3c 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) Dividing 1-digit divisor and quotient with remainder.
(3c) Division equation with ÷ sign; facts with no remainder
(4a) 1-digit divisor; 2- or 3-digit dividend, 2-digit quotient; no remainder.
(4b) 1-digit divisor; 2- or 3-digit dividend, 2-digit quotient; remainder.
(4c) 1-digit divisor; 2- or 3-digit dividend, 2-digit quotient with zero; remainder.
not yet completed levels–coming soon
(4d) 1-digit divisor; 3- or 4-digit dividend, 3-digit quotient.
(4e) 1-digit divisor; 3- or 4-digit dividend, 3-digit quotient with zero.
(4f) 1-digit divisor; 4- or 5-digit dividend, 4-digit quotient.
(4g) Rounding to the nearest ten.
(4h) 2-digit divisor; 1- or 2-digit quotient, all estimation yields correct quotient.
(4i) 2-digit divisor with incorrect estimated quotients.
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 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.
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