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Multiplication–Learning Computation
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 3rd 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 (4th 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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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 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.
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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 3rd 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 (4th 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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Mixed 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: When you add a positive number OR subtract a negative number, go UP.
Rule 2: When you subtract a positive number OR add a negative number, go DOWN.Students learn how these rules play out when starting with a positive number and a negative number, gradually learn these two variations of all four types of problems. They learn to solve a problem type using the number line and then to recognize the pattern of each problem type by working several examples of each type. This practice gives them a chance to build fluency with each problem type as they work with their partner on the top half of the page. 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 meet or beat their goal from the special writing speed test for mixed integers.
8 online lessons teach students how each type of problem is solved and why it is correct.
(1) Mixed Integers Set A1 Positive add a positive
(2) Mixed Integers Set A2 Positive subtract a positive
(3) Mixed Integers Set D Negative add a positive
(4) Mixed Integers Set G Negative subtract a positive
(5) Mixed Integers Set J Negative subtract a negative
(6) Mixed Integers Set M Positive subtract a negative
(7) Mixed Integers Set P Positive add a negative
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