Learning to Subtract Integers (positive and negative numbers)

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.  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.

Note that the number for each skill gives the grade level as well as indicating the teaching sequence.  Skill 2a is a 2^nd 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 (4^th 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.
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After becoming fluent with multiplication facts the best way for students to retain the knowledge of those facts is by doing multiplication computation.  If students have not been taught multiplication 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 3^rd grade skill and after skill 3e 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 (4^th Edition) Pearson Education: Columbus, OH.

(3b) Multiplying 1-digit times 2-digit; no renaming

(3c) Multiplying 1-digit times 2-digit; carrying

(3d) Multiplying 1-digit times 2-digit, written horizontally.

(3e) Reading and writing thousands numbers, using commas.

(4a) Multiplying 1-digit times 3-digit

(4b) Multiplying 1-digit times 3-digit; zero in tens column

(4c) Multiplying 1 digit times 3 digit, written horizontally

(4d) Multiplying 2-digits times 2-digits.

(4e) Multiplying 2-digits times 3-digits.

(5a) Multiplying 3-digits times 3-digits.

(5b) Multiplying 3-digits times 3-digits; zero in tens column of multiplier.

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.
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Skip counting is the best way for students to prepare for multiplication. Students practice with a partner who has the answers. Because of the way the rockets go around the page, students and their checkers will have to pick up the pages and turn them as they are working. You’ll be able to see if they are really engaged and they will have fun turning the page around. Students learn part of each sequence on a page, then the next page they learn the rest. For example: in Set O students learn to count by 3s to 12, then in Set P they learn to count by 3s to 21, and then in Set Q they learn to count by 3s to 30. The test in the center has them write the count-by series they have learned for one-minute and they need to meet or beat their best–just like the rest of Rocket Math. Here is the sequence students will learn in this order: 2s, 5s, 10s, 9s, 4s, 25s (so they can count quarters), 3s, 8s, 7s, and 6s. Probably our most fun product.
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(12) Make certain students remember how to make corrections when practicing Rocket Math. Display these 18 x 24 inch posters on the walls in a dozen classrooms and use it to teach students how to make those all-important corrections for errors and hesitations. A $216 value.