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

The Beginning Numerals Learning Track is one of 26  included in the Universal Level Worksheet program subscription, which is available to try for 60 days.

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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The Identifying Fractions Learning Track is one of 26 included in a Universal Level Worksheet program subscription, which is available to try for 60 days.

Identifying Fractions is a Learning Track to ensure that students have a firm and correct understanding of fractions.  This will prepare them well for all subsequent work in fractions.  They will learn the essential rule about what the numerator and denominator mean, although they won’t be working with those terms.  They just learn through examples, practiced over and over.

The number on the top tells how many parts are shaded.  The number on the bottom indicates the number of parts in a whole.  If a whole is not divided into parts, it is a whole number.

Right from the beginning of Set A students will encounter improper fractions and mixed numbers.  They will see examples of every fraction first at the top of the page before they are asked to identify it on their own. You see that students see the fraction, see the words for how we say it and they see the fraction they are to write.

Unlike other Rocket Math programs, the test and the practice items are the same.  Of course the students have a page without the answers, while their partner holds the answer key. Students practice by saying aloud to their partner the fractions shown in the test.  Then they take the test on those same items, but write the answer.

The fractions that students become familiar with include, halves, thirds, quarters, fifths, sixths, eighths, tenths and twelfths.  They see improper fractions and mixed number with every denominator.  In the beginning with the smaller denominators students see a variety of shapes for each denominator, so they learn that the identity of a fraction only has to do with the number of parts in a whole, not the shape of the display.  You can see thirds as cubes and as circles and as rectangles in the examples to the right.

When students are eventually introduced to eighths, tenths and twelfths we don’t want to slow them down by having to laboriously count the number of parts in each figure.  So the eighths are always displayed as two sets of four rectangles on top of each other.  Tenths are displayed as two columns of five blocks with little numbers in them.  Twelfths are always displayed as three sets of four rectangles on each other.  Students should notice these conventions so they can quickly identify the number of parts in those figures without having to count them.

Identifying fractions has its own writing speed test, to be sure that student goals are individualized to their writing speed.  By the time students complete Set Z in this program they will have a strong understanding of fractions that will be fluent.  There are even 2-minute timings you can give every week or two for them to chart their progress as they get faster.  This is a great program for students of any grade from second grade on up who have finished the basics for their grade level.  It will really put them in good shape when dealing with fractions in later years.

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The “Add-Subtract-Fact-Families-to-10” Learning Track is one of 26 included in a Universal Level Worksheet program subscription, which is available to try for 60 days.

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. You can see to the left the 25 examples of fact families taught in this program starting with Set A; 3+1, 1+3, 4-1 & 4-3.  The sheet shows the sequence of learning facts in the new Rocket Math  program Fact Families 1s-10s (+, -).  Each set that students learn from A to Y 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.

Best fit for first grade.  I separated out the 1s through 10s facts from the 11s-18s, because these 25 families are just enough for one Rocket Math program.  It is a good and sufficient accomplishment for first grade.  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.

Add-Subtract Fact Families to 10 is the first half.  The rest of the addition and subtraction fact families, which students could learn in 2nd grade, are the Add-Subtract Fact Families 11 to 18.  I most sincerely want students to be successful and to enjoy (as much as possible) the necessary chore of learning math facts to automaticity.

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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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