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

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This is a program 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.

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Dictating Sentences is spelling with a twist.  Instead of spelling one word at a time, in Dictating Sentences (now part of the Universal Level Rocket Math Worksheet Program) students are asked to write an entire sentence from memory.  They work in pairs and their tutor has the student repeat the sentence until it is learned.  Then the student has to write the whole sentence from memory.  It turns out this is considerably harder than writing words on a spelling test, so it is challenging practice, and does a lot to help students develop automaticity with spelling.

If you have to stop and think of the spelling of a word  while you are trying to write, it distracts you from thinking about what you are trying to write.  Students are more successful and better able to show what they know and better able to focus on learning when their tool skills have developed to the level of automaticity.

Daily practice develops automaticity.  Developing automaticity with math facts and with spelling requires a lot of practice.  Daily practice is best and a few minutes a day is optimal.  That is why Rocket Math is designed the way it is–to provide that daily practice.  So Dictating Sentences gives each member of the pair ten minutes a day of practice writing sentences composed of words they know how to spell.

Working in pairs.  As you know from Rocket Math practice, students enjoy working in pairs.  And when one partner has an answer key the practice can be checked and corrected.  Sound research shows that immediate correction and editing of misspelled words is the fastest way to learn the correct spelling, so that’s what we have the student tutor do.  After each sentence is written every word is checked and practiced again until it is correct.

Mastery learning. The program is structure so that all the words are learned to the level of automaticy.  Students keep working on a sentence until it can be written without any errors.  They work on the same lesson for as many days as is needed for them to spelling every word perfectly in all three sentences.  Each sentence persists for two or three lessons, so that the student is required to write it from memory and spell every word perfectly for several days in a row.

500 Most common words.  Dictating sentences systematically practices the 500 most common words that students need in their writing.  It includes all of Rebecca Sitton’s 400 Core Words.  It also includes the 340 words that children most need for writing according to writing researchers Harris and Graham.   When students know these words to the level of automaticity, they will be able to write fluently and easily.

Earning points by being correct and going fast.  Students earn two points for every word that is spelling correctly the first time.  Every word on which there is an error is worked on until it too can be spelled correctly, earning one point.  The faster students go during their ten minutes, the more points they can earn.  Students graph the amount of points earned and try to beat their own score from previous days.  Teams can be set up and competition for the glory of being on the winning team can enhance the motivation.

Individual Placement.  There is a placement test.  Students begin at the level where they first make a mistake.  Student partners do not need to be at the same level, so every student can be individually placed at the level of success.

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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 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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