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Home Uncategorized extras Multiplication–Learning Computation

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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  • Uncategorized extras Add to 20 (e.g., 13+6, 4+11, 15+5)

    These are the rest of the Addition facts that the Common Core suggests that students be able to compute mentally such as 11 + 7, 4 + 13, and 16 + 3. These obviously build on the basic single digit facts such as 1 + 7, 4 + 3, and 6 + 3. 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 Add to 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 Add to 20 program.  Otherwise the program is exactly the same as the basic Addition Rocket Math program and uses the same forms–that can be found in the forms and information drawer.

     

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  • Uncategorized extras Multiplication 1s through 9s [BASIC]

    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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  • Uncategorized extras Mixed Integers (adding and subtracting positive and negative numbers)

    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

    (8) Mixed Integers Set S Negative add a negative

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  • Uncategorized extras Rocket Writing for Numerals

    Rocket Writing for Numerals prepares students to write numerals efficiently, quickly and legibly. There are 72 pages of practice divided into four chapters which gradually increase in difficulty. (The red “Chapter 1, Chapter 2” etc don’t show in the actual program!)

    • Chapter 1 starts with simply having students tracing the numerals and learning to form them in the correct manner. Students work through each of the numerals and practice them in concert with other previously learned numerals.
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