Learning to Subtract Integers (positive and negative numbers)

The Addition 1s-9s Learning Track is one of the 4 included in the Basic Level subscription.

These are the basic single digit Addition 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 B, I have outlined the new facts in red.

Students practice orally with a partner. They read and answer 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.  The test includes only the facts learned up to this level.  Each student has individual goals based on writing speed.  Students cannot pass a level if there are any errors.   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.   Below you can see the sequence of facts that will be learned in the Addition 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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The Division (1s-9s) Learning Track is one of four included in the Basic Level Worksheet Program subscription.

These are the basic single digit Division 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 D, 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.   Below you can see the sequence of facts that will be learned in the Division 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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The Subtract from 20 Learning Track is one of 26 included in the Universal Level Worksheet program subscription, which is available to try for 60 days.

These are the rest of the Subtraction facts that the Common Core suggests that students be able to compute mentally such as 18-15, 15-5, and 19-8. These obviously build on the basic single digit facts such as 8-5, 5-5, and 9-8. 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 Subtract from 20 Writing Speed Test to set new, lower, goals for your students.  To the left you can see the sequence of facts that will be learned in the Subtract from 20 program.  Otherwise the program is exactly the same as the basic Subtraction Rocket Math program and uses the same forms–that can be found in the forms and information drawer.

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The Subtraction–Learning Computation Learning Track is one of 26 included in a Universal Level Worksheet program subscription.

After becoming fluent with subtraction facts the best way for students to retain the knowledge of those facts is by doing subtraction computation.  If students have not been taught subtraction computation, Subtraction–Learning Computation breaks it down into 18 small, easy-to-learn steps that are numbered in a teaching sequence that leaves nothing to chance.  Even better the instructional materials include an assessment of all the skills in subtraction computation in order, so you can test the knowledge of the student(s) before beginning instruction to see where to start. You can use this assessment to find very specific “holes” in student skills and then have the exact problems and explanation to fill that hole.

Note that the number for each skill gives the grade level as well as indicating the teaching sequence.  Skill 3b is a 3^rd grade skill and after skill 3g is learned the next in the sequence, skill 4a is best taught in fourth grade.  Minor changes have been made, but for the most part, 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 (4^th Edition) Pearson Education: Columbus, OH.

(1b) Subtract from 2 digits; no renaming.

(2a) Subtract from 2digits; renaming required.

(2b) Subtract from 3 digits; borrow from 10s.

(3a) Subtract from 3 digits; borrow from 100s.

(3b) Subtract from 3 digits; borrow either place.

(3c) Subtract tens minus one facts.

(3d) Subtract from 3 digits; zero in 10s; borrow 10s or 100s.

(3e) Read and write thousands numbers, use commas.

(3f) Subtract from 4 digits; borrow from 1000s.

(3g) Subtract from 4 digits; borrow once or more.

(4a) Subtract from 4 digits; zero in 10s or 100s column

(4b) Subtract from 4 digits; zero in 10s column, 1 in 100s.

(4c) Subtract hundreds minus one facts.

(4d) Subtract from 4 digits; zero in 10s and 100s column.

(4e) Subtract 1, 2, or 3 digits from 1,000.

(4f) Subtract 5 and 6 digits with borrowing.

(5a) Subtract thousands minus one facts.

(5b) Subtract from a number with four zeroes.

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.  My favorite part is the rule students are taught for when to borrow (often confusing for students): Bigger bottom borrows.  Simple, easy-to-remember and consistently correct.  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.

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