Multiplication–Learning Computation

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 3^rd 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 (4^th 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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This is a beginning program for kindergarten students.  You are teaching them to count objects aloud and then match the word with the numeral.

Each worksheet begins with a demonstration of counting objects and circling the numeral that matches.  On Worksheet A there are two and three only to learn.  The teacher demonstrates (best with a document camera so all students can see) how she counts the objects and then points out that the answer is circled.

In the “You do” portion of the worksheet after learning the numerals with the teacher, the students are asked to count the items in each box and circle the correct number.  They are not asked to form the numerals–that’s numeral writing skill.  They just identify the numeral and circle it. Besides cute items there are also dice to count, fingers to count and hash marks to count–so students can learn multiple ways of keeping track of numbers.

Passing a level requires 100% accuracy.  Students who make any errors should be worked with until they can complete the worksheet independently and get all the items correct.

This will build strong beginning math skills for kindergarteners learning the meaning of numerals.  Combined with Rocket Writing for Numerals it will set students up for success in elementary math.

In the “We do” portion of the worksheet the teacher counts the stars first as a demo and then with the students.  Worksheet A you all just count 3 stars.   By Worksheet S the teacher and the students are  counting 12 stars together.

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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. This program is Part 2 of Fact Families, coming after Fact Families 1 to 10. You can see to the left the 18 examples of fact families taught in this program starting with Set A; 11-2, 11-9, 9+2, & 2+9.  The sheet shows the sequence of learning facts in the new Rocket Math  program Fact Families Part Two 11 to 18 (+, -).  Each set that students learn from A to R 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.

Part Two is a Best fit for second grade.  These facts come after the facts in 1 to 10, typically learned in first grade, so these are best for second grade.  The 25 fact families in 1s through 10s facts are just enough for one Rocket Math program.  It is a good and sufficient accomplishment for first grade.  With the 11 to 18 in Par Two for second grade there will be a lot of review.  In fact sets S through Z are all review. 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 Part Two 11 to 18 (+, -) to the Universal subscription in August of 2018 bringing the total number of programs in the Universal subscription to 19 (the basic four operations and 15 more!).  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 11 to 18 (+, -),  as to how it goes for the students.

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